LIBRARY 

OF  THE 

UNIVERSITY  OF  CALIFORNIA. 

GIFT    OF 


Class 


THE 


PACKARD 


COMMERCIAL  ARITHMETIC. 


S.    S.    PACKARD, 

PRESIDENT  OF  PACKARD'S  BUSINESS  COLLEGE,  NEW  YORK,  AUTHOR  OF  THE  BRYANT  AND 

STRATTON  BOOK-KEEPING  SERIES,  AND  OF  PACKARD'S  COMPLETE 

COURSE  OF  BUSINESS  TRAINING, 

AND 

BYRON    HORTON,    A.M., 

PRINCIPAL  OF  THE  MATHEMATICAL  DEPARTMENT  OF  PACKARD'S  BUSINESS  COLLEGE. 


NINTH     EDITION. 


NEW    YORK: 
S.    S.    PACKARD,    805    BROADWAY. 

1883. 


THE.  PACKARD   COMMERCIAL  ARITHMETIC. 

COMPLETE    EDITION,   328  PAGES,   OCTAVO. 

SCHOOL    EDITION,   276   PAGES,    12MO. 

KEY    TO    COMPLETE    EDITION  (FoR  TEACHERS),  $1.00. 

KEY    TO    SCHOOL    EDITION— IN  PREPARATION. 

The  complete  edition  is  published  both  with  and  without  answers.      Unless 
otherwise  ordered,  books  without  answers  will  be  sent. 


COPYRIGHT,  1882, 
BY  S.   S.   PACKARD  AND  BYRON  HORTON. 


Electrotyped  by  Printed  by 

SMITH  &  McDouoAL.  RUSSELL  BROTHERS 


PREFACE. 


THE  question  as  to  whether  a  new  Commercial  Arithmetic  was 
called  for,  is  answered  in  the  ready  sale  which  has  attended 
the  publication  of  this  volume.  It  does  not  necessarily  argue  that 
other  arithmetics  have  failed  to  meet  a  large  popular  demand,  or 
that  those  who  use  them  are  dissatisfied  with  them.  It  simply 
emphasizes  the  fact  that  what  may  suit  one  intelligent  teacher  will 
not,  for  that  reason  alone,  suit  another  ;  and  nothing  could  make 
this  point  clearer  than  to  state,  what  is  really  true,  that  all  the 
Commercial  Arithmetics  that  have  appeared  during  the  past  ten 
years  have  been  prepared  by  active  teachers,  who  required  cer- 
tain things  in  their  own  work  not  to  be  found  in  existing  books. 
There  are  few,  if  any,  text  books  that  could  not,  in  some  respects, 
be  changed  to  advantage  by  those  who  use  them  ;  and  the  main 
reason  why  there  are  not  fifty  text  books  where  there  is  but  one 
is  a  reason  of  economy,  rather  than  of  inability  of  teachers  to  pre- 
pare their  own  books,  or  even  of  entire  satisfaction  with  the  books 
in  use. 

It  is  worthy  of  notice  that,  in  the  line  of  commercial  text  books 
particularly,  there  is  a  growing  tendency  to  authorship  on  the  part 
of  wide  awake  teachers  ;  so  much  so  that  there  are  to-day  twenty 
treatises  on  book-keeping  where  there  was  one  twenty  years  ago ; 
and  in  the  line  of  commercial  mathematics,  commercial  law  and 
practical  grammar,  one  can  safely  calculate  on  a  new  book  every 
six  months.  Nobody  has  a  right  to  complain  of  this  tendency. 
It  should,  in  fact,  give  great  satisfaction  to  all  who  are  interested 
in  practical  education  ;  for  it  not  only  speaks  of  the  growing 
energy  and  intelligence  of  the  teachers  who  have  this  education  in 
charge,  but  especially  of  the  appreciation  of  the  public,  through 
whose  encouragement  alone  such  worthy  ambition  can  be  gratified. 

The  authors  of  this  book  do  "not  claim  to  have  discovered,  all 
at  once,  that  nobody  hitherto  has  had  the  ability  to  prepare  an 
arithmetic,  or  that  it  was  impossible  longer  to  utilize  the  books 


183983 


iv  PREFA  OE. 

that  have  served  the  purposes  of  the  past.  They  do  not  even 
claim  that  their  book  is  better,  or  worse,  than  any  or  all  of  its  pre- 
decessors ;  they  claim  only  that  it  is  different  from  any  of  them, 
and  in  this  difference  lies  their  only  excuse  for  its  appearance. 
The  book  was  written  to  supplv  a  known  want  in  a  single  school, 
with  the  feeling,  also,  that  other  schools,  having  felt  a  similar  want, 
might  find  it  met,  in  some  measure,  through  the  efforts  here  put 
forth.  In  fact,  a  large  number  of  teachers  have  already  expressed 
such  satisfaction  in  a  practical  way,  and  there  are  doubtless  others, 
on  the  point  of  issuing  their  own  books,  who,  upon  a  close  exam- 
ination of  this,  will  find  it  so  well  suited  to  their  purpose  that  they 
will  be  induced  to  lay  aside  for  a  time  their  unfinished  manu- 
script, and  possibly  to  defer  publication  indefinitely.  There  is  no 
desire  on  the  part  of  the  authors  of  this  book  to  discourage  the 
publication  of  new  arithmetics  ;  but  they  are  quite  willing  to  do 
what  lies  in  their  power,  in  connection  with  their  fellow-authors 
already  in  the  field,  to  satisfy  teachers  so  fully  that  they  will  find 
no  good  excuse  for  diverting  their  energies  from  the  great  work  of 
oral  instruction,  but  will  seek  rather  to  give  to  it  new  zest,  with 
the  consciousness  that  others  are  both  willing  and  able  to  relieve 
them  from  the  irksomeness  and  risk  of  book-making. 

It  is  not  deemed  necessary  to  point  out  with  particularity  the 
peculiar  merits  or  demerits  of  the  book.  Both  will  be  readily  dis- 
cerned by  those  who  use  it,  and  those  who  do  not  use  it  will  care 
very  little  about  them.  We  will  only  say  that  it  is  not  a  re- 
hash of  any  book  or  books  that  have  gone  before  it,  and  that  in  not 
a  single  instance  have  the  authors  relied  for  their  statistics,  their 
statements  of  local  laws  and  customs,  or  any  of  their  facts,  upon 
other  authors,  either  of  the  present  or  the  past,  but  have  uniformly 
obtained  their  information  from  the  highest  authentic  sources. 
And,  moreover,  they  propose  to  keep  open  these  avenues  of  infor- 
mation, and  to  revise  all  future  editions  closely  in  reference  to  any 
changes  that  may  occur. 

It  is  but  justice  to  say  that  the  main  work  of  authorship  has 
been  done  by  the  one  whose  name  stands  second  on  the  title  page, 
which  renders  it  possible  to  add  that  it  has  been  conscientiously 
and  faichfully  done. 

NEW  YORK,  October  2,  1882. 


CONTENTS. 


PACK 

PROPERTIES  OF  NUMBERS 1 

Prime  Factors .  . 3 

Common  Divisors 4 

Common  Multiples 6 

Cancellation 8 

REVIEW  EXAMPLES 11 

FRACTIONS 14 

Reduction 16 

Addition 20 

Subtraction 22 

Multiplication ...  23 

Division 27 

REVIEW  EXAMPLES 32 

DECIMALS 36 

Reduction 40 

Addition 41 

Subtraction .      43 

Multiplication 44 

Division 45 

REVIEW  EXAMPLES 46 

DENOMINATE  NUMBERS 49 

Divisions  of  Time 49 

Linear  Measures 51 

Square  Measures 52 

Cubic  Measure 54 

Liquid  Measures 56 

Dry  Measure 66 

Measures  of  Weight 57 

Circular  Measure 59 

United  States  Money 60 

English  Money  ....    63 

Foreign  Moneys  of  Account 64 

Reduction  of  Denominate  Integers 65 

Reduction  of  Denominate  Fractions 67 

Addition 71 

Subtraction 72 

Multiplication 74 

Division 75 

Longitude  and  Time 75 

THE  METRIC  SYSTEM 77 

Linear  Measure 78 

Square  Measure 79 

Cubic  Measure 80 

Dry  and  Liquid  Measure 81 

Weight 82 

Table  of  Equivalents 84 

Approximate  Rules 85 

FOREIGN  WEIGHTS  AND  MEASURES 88 


Vi  CONTENTS. 

PAGE 

REVIEW  EXAMPLES 90 

PERCENTAGE 95 

DISCOUNTS 100 

BILLS. 102 

COMMISSION  AND  BROKERAGE 110 

PROFIT  AND  Loss 114 

INTEREST 117 

Accurate  Interest 127 

PROBLEMS  IN  INTEREST 129 

To  find  the  Rate  129 

To  find  the  Time 130 

To  find  the  Principal,  the  Interest,  Time,  and  Rate  being  given. . .   131 
To  find  the  Principal,  the  Amount,  Time,  and  Rate  being  given. . .  132 

PRESENT  WORTH  AND  TRUE  DISCOUNT 133 

REVIEW  EXAMPLES 134 

ANNUAL  INTEREST ]  37 

COMPOUND  INTEREST 139 

COMMERCIAL  PAPER 143 

BANK  DISCOUNT 149 

PARTIAL  PAYMENTS « 153 

United  States  Rule 153 

Mercantile  Rules 156 

Connecticut  Rule 159 

New  Hampshire  Rule 161 

Vermont  Rule  162 

RATIO  AND  PROPORTION 163 

INSURANCE 166 

Fire  Insurance 168 

Marine  Insurance 169 

EXCHANGE 174 

Domestic  Exchange 175 

Foreign  Exchange 178 

EQUATION  OF  ACCOUNTS 187 

When  the  items  are  all  debits  or  all  credits 187 

When  the  account  contains  both  debit  and  credit  items 198 

Equation  of  Accounts  Sales 203 

ACCOUNTS  CURRENT 207 

STOCKS  AND  BONDS 216 

Government  Bonds 218 

New  York  Stock  Exchange 221 

TAXES 235 

DUTIES 238 

PARTNERSHIP 249 

NATIONAL  BANKS 264 

SAVINGS  BANKS 269 

LIFE  INSURANCE 273 

GENERAL  AVERAGE 280 

CLEARING  HOUSES 285 

DETECTION  OF  ERRORS  IN  TRIAL  BALANCES 290 

REVIEW  EXAMPLES 291 

APPENDIX 296 

Drill  Exercises 296 

Short  Method  of  finding  the  Balance  of  an  Account 298 

Short  Methods  in  Multiplication 299 

Short  Methods  of  Division 310 

Explanatory  Notes 312 


V     OF  THE 

I    UNIVERSITY  ) 


COMMERCIAL   ARITHMETIC. 


PROPERTIES    OF    NUMBERS. 

DEFINITIONS. 

1.  A  Unit,  or  Unity,  is   one,  or  a  single  thing;   as  one, 
one  foot,  one  dollar. 

2.  A  Number  is  a  unit,  or  a  collection  of  units ;  as  one, 
four,  three  feet,  five  dollars. 

3.  All  numbers  are  either  integral  or  fractional,  abstract  or 
concrete. 

4.  An  Integral  Number,  or  Integer  is  a  number  which 
expresses  whole  things  ;  as  two,  four  gallons,  seven  dollars. 

5.  A    Fractional    Number,  or   Fraction    is  a  number 
which  expresses  one  or  more  equal  parts  of  a  unit ;  as  one-half, 
three-fourths. 

6.  An   Abstract   Number  is   a  number  which  does  not 
refer  to  any  particular  object ;  as  one,  six,  ten. 

7.  A  Concrete  Number  is  a  number  applied  to  an  object, 
or  quantity  ;  as  three  apples,  five  pounds,  ten  dollars. 

8.  Integral  numbers  are  either  odd  or  even,  prime  or  com- 
posite. 

9.  An   Odd   Number  is  a  number  whose  unit  figure  is 
1,  3,  5,  7,  or  9 ;  as  7,  21,  39. 


2  PROPERTIES     OF    LUMBERS. 

1C.   An  Even  Number  is  a  number  whose  unit  figure  is 
0,  2,  4,  6,  or  8  ;  as  6,  40,  74. 

11.  A  Prime  Number  is  a  number  which  can  be  exactly 
divided  only  by  itself  and  unity ;  as  1,  7,  13,  29. 

12.  Numbers  are  prime  to  each  other  when  no  integral 
number  greater  than  1  will  divide  each  without  a  remainder. 

Numbers  that  are  prime  to  each  other  are  not  necessarily  prime  numbers. 
Thus,  25  and  28  are  prime  to  each  other,  but  they  are  not  prime  numbers. 

13.  A    Composite   Number   is  a  number  which  can  be 
exactly  divided  by  other  integers  besides  itself  and  unity. 

Thus  28,  the  product  of  4  and  7,  is  a  composite  number.     It  is  exactly 
divisible  by  4  and  7. 

DIVISIBILITY    OF    NUMBERS. 

14.  An  Exact  Divisor  of  a  number  is  any  number  that 
will  divide  it  without  a  remainder. 

Thus  2,  3,  4,  6,  8,  and  12  are  exact  divisors  of  24. 

15.  A  number  is  said  to  be  divisible  by  another  when  the 
latter  will  divide  the  former  without  a  remainder.     Any  number 
is  divisible 

1.  By  2,  if  it  is  an  even  number ;  ae  6,  28,  and  32. 

2.  By  3,  if  the  sum  of  its  digits  is  divisible  by  3  ;   as  849 
(8  +  4+9  =  21,  21  is  divisible  by  3),  7323,  and  47892. 

3.  By  4,  if  the  two  right-hand  figures  are  ciphers,  or  express  a 
number  divisible  by  4  ;  as  1100,  216,  and  7328. 

4.  By  5,  if  the  right-hand  figure  is  0  or  5  ;  as  40  and  135. 

5.  By  6,  if  it  is  an  even  number  and  the  sum  of  its  digits  is 
divisible  by  3  ;  as  216,  840,  and  732. 

6.  By  8,  if  the  three  right-hand  figures  are  ciphers,  or  express 
a  number  divisible  by  8  ;  as  3000  and  7168. 

7.  By  9,  if  the  sum  of  its  digits  is  divisible  by  9  ;  as  216,  783, 
and  12348. 


PRIME     FACTORS. 


PRIME    FACTORS. 

16.  The  Factors  of  a  number  are  those  numbers  which 
multiplied  together  will  produce  the  number. 

Thus  4  and  7 ;  2  and  14 ;  2,2,  and  7  are  factors  of  28.     The  number  itself 
and  unity  are  not  regarded  as  factors. 

The  factors  of  a  number  are  also  the  exact  divisors  of  it. 

17.  A  Prime  Factor  is  a  prime  number  used  as  a  factor. 

Thus,  2,  2,  and  7  are  the  prime  factors  of  28.     4  is  a  factor  of  28,  but  not 
&  prime  factor. 

18.  To   find   all   the   prime   factors  of  a   composite 
number. 

Ex.  What  are  the  prime  factors  of  6930. 

OPERATION.  ANALYSIS.— Any  prime  number  that  is  an  exact  divi- 

2  )  6930  sor  of  the  given  number  is  a  prime  factor  of  it.     Divide 
„  ,  qj/»-  the  given  number  by  2  (15,  1),  the  least  prime  divisor  of 

it,  obtaining  the  quotient  3465.     Next,  divide  this  quo- 

3  )  1155  tient  successively  by  3  (15,  2),  3,  5  (15,  4),  and  7.     The 
5  )  385  last  (luotient  11  is  a  Prime  number  and  therefore  a  prime 

factor.    The  several  divisors  2,  3,  3,  5,  7  and  the  last  quo- 
«  )  '  «  tient  11  are  the  prime  factors  required. 

11  2x3x3x5x7x11  =  6930. 

19.  RULE. — Divide  by  the  least  prime  ninriber  which 
will  divide  the  given  number  without  a  remainder.     In 
like  manner  divide  the  resulting  quotient,  and  continue 
the  division  until  the  quotient  is  a  prime  number.     The 
several  divisors  and  the  last  quotient  are  the  prime  factors. 


EXAMPLES. 
2O.  Resolve  the  following  numbers  into  their  prime  factors  : 

1.  3465.               7.     6552.             13.  8192.  19.  6660. 

2.  3003.              8.     7826.             14.  6561.  20.  2448. 
8.     4158.               9.     6006.             15.  3125.  21.  8525. 

4.  3150.             10.     5368.             16.  1800.  22.  9936. 

5.  3675.             11.     3825.             17.  1935.  23.  9576. 

6.  2310.             12.     5324.             18.  2475.  24.  5075. 


PROPERTIES     OF     NUMBERS. 


COMMON     DIVISORS. 

21.  A  Common  Divisor,  or  Common  Measure,  of  two 
or  more  numbers  is  any  number  that  will  divide  each  without 
a  remainder  ;  hence  it  is  a  common  factor  of  each  of  them. 

22.  The    Greatest    Common   Divisor  of   two   or   more 
numbers  is  the  greatest  number  that  will  divide  each  without  a 
remainder  ;  hence  it  is  their  greatest  common  factor. 

Thus,  2,  3,  4,  and  12  are  common  divisors  of  36,  48,  and  60 ;  12  is  their 
greatest  common  divisor. 

23.  PRINCIPLE. — TJie  greatest  common  divisor  of  tivo  or  more 
numbers  is  the  product  of  all  their  common  prime  factors. 

24:.  To  find  the  greatest  common  divisor  of  two  or 
more  numbers. 

Ex.  What  is  the  greatest  common  divisor  of  168,  252,  and  420  ? 

FIRST  OPERATION. 

*  *  *          * 

168  =  2x2x2x3x7  ANALYSIS. — Resolve    the    numbers    into 

*  *      *  *  their  prime  factors.     The  product,  84,  of  the 

common  factors  2,  2,  3,  and  7  is  the  greatest 
420  =  2x5x3x5x7  common  divisor.    (Prin.) 

2x2x3x7  =  84. 

SECOND  OPERATION.  ANALYSIS. — Divide  the  given  numbers  by 

4  )  168,   252,   420  any  number  that  will  divide  them  all  without 

<y~\~AV       fiQ     7n*  a  remamder>  anc*  Divide  the  quotients  in  the 

)  4%,      bo,    105  same  manner  until  the  last  quotients  have  no 

3)6,        9,      15  common  divisor.     Since  4  will  divide  all  the 

I         o I  given  numbers,  and    3    and   7   will    divide 

successively   the    resulting    quotients,   their 

4x7x3  =  84.  product,  84,  is  a  common  divisor  of  the  given 

numbers.     Since  the  last  quotients  have  no 
common  divisor  or  factor,  84  is  the  greatest  common  divisor. 

25.  RULE. — Resolve  the  numbers  into  their  prime  fac- 
tors. The  product  of  the  factors  common  to  all  the  numbers 
will  be  the  greatest  common  divisor.  Or, 

Divide  the  given  numbers  by  any  factor  that  will  divide 
all  of  them  without  a  remainder.  In  H7ce  manner  divide 


COMMON     DIVISORS.  5 

the  resulting  quotients,  and  continue  the  division  until  the 
quotients  have  no  common  factor,  ^e  product  of  the  sev- 
eral divisors  will  be  the  greatest  common  divisor. 

EXAMPLES. 

26.  Find  the  greatest   common   divisor   of    the    following 
numbers  : 

1.  24,    36,  and     48.  9.     108,  144,  and  360. 

2.  35,    56,  and     70.  10.     144,  336,  and  240. 
8.     42,    56,  and     28.  11.     165,  550,  and  220. 

4.  30,    60,  and     75.  18.  792,  144,  and  216. 

5.  64,    96,  and  128.  13.  405,  243,  and  324. 

6.  66,  198,  and  330.  14.  378,  126,  and  252. 

7.  90,  150,  and  210.  15.  375,  625,  and  250. 

8.  84,  420,  and  126.  16.  288,  720,  and  864. 

27.  To   find   the   greatest    common    divisor  of  two 
numbers  when  they  are  not  readily  factored. 

28.  PRINCIPLES. — 1.  If  the  smaller  of  tivo  numbers  is  a  divisor 
of  the  greater,  it  is  their  greatest  common  divisor. 

2.  A  common  divisor  of  two  numbers  is  a  divisor  of  their  sum, 
and  also  of  their  difference. 

3.  A  divisor  of  a  number  is  a  divisor  of  any  multiple  of  that 
number. 

29.  RULE. — Divide  the  greater  number  by  the  smaller, 
and  divide  the  last  divisor  by  the  remainder;  and  so  con- 
tinue until  there  is  no  remainder.     The  last  divisor  will  be 
the  greatest  common  divisor. 


~3  ' 


NOTES. — 1.  When  the  greatest  common  divisor  of  more  than  two  numbers 
is  required,  find  the  greatest  common  divisor  of  the  smallest  two  first,  and  of 
this  greatest  common  divisor  and  the  next  greater,  and  so  on,  until  all  tlie 
numbers  are  used.  The  last  divisor  will  be  the  greatest  common  divisor  of 
all  the  given  numbers. 

2.  If,  at  any  step  in  the  process,  a  prime  factor  appear  that  is  not  common 
to  all  the  numbers,  it  may  be  rejected.     (See  second  operation  of  example.) 

3.  If  the  remainder  at  any  time  is  a  prime  number,  and  it  is  not  contained 
in  the  last  divisor,  there  is  no  common  divisor  greater  than  1 ;  it  will  there- 
fore be  useless  to  further  jontinue  the  division. 


6  PROPERTIES     OF    NUMBERS. 

Ex.  Find  the  greatest  common  divisor  of  391  and  437. 

OPERATIONS.  DEMONSTRATION.  —  Since 

391  )  437  (1  23  is  a  divisor  of  46,  it  is  a  di- 

391  Or,  visor  of  368> a  multiple  of  46 

~7«  \  QQ1    /  Q  9  \  K  «  (Prin-  3)' '    ShlCe  23  1S  a  diviS01' 

of  itself  and  368,  it  is  a  divisor 

368  23)391(17       of   their  sum,   391   (Prin.  2). 

23  )  46  (  2  23  Since  23  is  a  divisor  of  46  and 

.„  391,  it  is  a  divisor  of  their  sum, 

437.     23  is  therefore  a  common 

0  161  divisor  of   391   and    437,   the 

rt  given  numbers. 

The  greatest  common  di- 
visor of  391  and  437,  whatever  it  may  be,  is  a  divisor  of  their  difference,  46 
(Prin.  2) ;  also  of  368,  a  multiple  of  46  (Prin.  3) ;  also  of  23,  391  —  368 
(Prin.  2).  Since  the  divisor  of  a  number  cannot  be  greater  than  itself,  the 
greatest  common  divisor  of  the  given  numbers  cannot  be  greater  than  23. 
23  is  therefore  the  greatest  common  divisor. 

3O.  Find  the    greatest    common  divisor  of  the    following 
numbers  : 

1.  319  and  377.  6.  744,  984,  and  522. 

&  259  and  629.  7.  391,  667,  and  920. 

3.  589  and  713.  8.  451,  481,  and  737. 

4.  903  and  989.  9.  504,  756,  and  252. 
6.  611,  799,  and  987.                 10.  425,  748,  and  561. 


COMMON     MULTIPLES. 

31.  A  Multiple   of  a  number  is  a  number  that  is  exactly 
divisible  by  it ;  or,  it  is  any  product  of  which  the  given  number 
is  a  factor. 

32.  A  Common  Multiple  of  two  or  more  numbers  is  a 
number  that  is  exactly  divisible  by  each  of  them. 

33.  The  Least  Common  Multiple  of  two  or  more  num- 
bers is  the  least  number  that  is  exactly  divisible  by  each  of  them. 

Thus,  12,  24,  36,  and  48  are  common  multiples  of  4  and  6;   12  is  their 
least  common  multiple. 


COMMON    MULTIPLES.  7 

34.  PRINCIPLES. — 1.  A  multiple  of  a  number  contains  all  the 
prime  factors  of  that  number. 

2.  A  common  multiple  of  two  or  more  numbers  contains  all  the 
prime  factors  of  each  of  those  numbers. 

3.  The  least  common  multiple  of  two  or  more  numbers  contains 
all  the   prime  factors  of  each  of  the  numbers,    and  no  other 
factors. 

35.  To   find  the   least  common  multiple  of  two  or 
more  numbers. 

Ex.    What    is    the  least  common  multiple   of    12,   18,  20, 
and  40? 

FIRST  OPERATION.  ANALYSIS.— Since  40,  a   multiple 

12  =  2x2x3  of  20,  contains  all  the  prime  factors  of 

18  =•  2  X  3  X  3  20,  the  number  20  may  be  omitted  in 

AQ  2x2x2x5  *ne  oPera^on-     Resolve  the  numbers 

into  their  prime   factors.     The    least 

2x2x2x3x3x5  =  360         common  multiple  must  contain  2  as  a 

factor  3  times  in  order  to  be  divisible 

by  40  ;  it  must  contain  3  as  a  factor  twice  in  order  to  be  divisible  by  18 ;  and 
it  must  contain  5  as  a  factor,  in  order  to  be  divisible  by  40.  360,  the  product 
of  the  factors  2,  2,  2,  3,  3,  and  5,  is  the  least  common  multiple  of  the  given 
numbers,  since  it  contains  the  different  factors  the  greatest  number  of  times 
that  they  occur  in  the  given  numbers,  and  no  other  factors  (Prin.  3). 

SECOND  OPERATION.  ANALYSIS. — The  factors  of    the   re- 

2)12,      18,      40  quired  multiple  may  be  selected  by  the 

2  \  Q         Q       OQ  following  process.     Divide  the  given  num- 

bers by  any  prime  number  that  will  divide 

3)3,        9,  two  or  more  of  them,  writing  the  quo- 

-^         3       10  tients  and  the   undivided  numbers  be- 

neath.    Treat  the  resulting  numbers  in 

2x2x3x3x10  =  360         like  manner,   and  continue   the  process 

until  no  two  of  the  numbers  have  a  com- 
mon factor  or  divisor.  The  product  of  the  several  divisors  and  the  remaining 
quotients  and  undivided  numbers  will  be  the  least  common  multiple. 

36.  EULE. — Resolve  the  given  numbers  into  their  prime 
factors,     ^e  product  of  the  different  prune  factors,  taking 
each  factor  the  greatest  number  of  times  it  appears  in  any 
of  the  numbers,  will  be  the  least  common  multiple.     Or, 


8  PROPERTIES     OF    NUMBERS. 

Divide  the  given  numbers  T}y  any  prime  number  (see 
Note  2)  that  will  exactly  divide  two  or  more  of  them,  writing 
the  quotients  and  undivided  numbers  beneath.  Repeat  the 
operation  with  the  resulting  numbers  until  there  is  no  exact 
divisor  of  any  two  of  them.  The  product  of  the  several 
divisors  and  the  last  quotients  and  undivided  numbers  will 
be  the  least  common  multiple. 

NOTES. — 1.  In  the  operation,  reject  such  of  the  smaller  numbers  as  are 
divisors  of  the  larger;  also  reject  such  of  the  quotients  and  undivided  num- 
bers as  are  divisors  of  the  others. 

2.  Divide  by  composite  numbers  when  they  are  exact  divisors  of  all  the 
numbers. 

EXAMPLES, 

37.  Find  the  least  common  multiple  of  the  following  numbers : 

1.  2,  3,  4,  5,  and  6.  15.  18,  24,  and  36. 

2.  8,  10,  12,  and  15.  16.  10,  24,  and  32. 

3.  12,  15,  18,  and  24.  17.  16,  18,  and  20. 

4.  6,  10,  15,  and  30.  18.  24,  36,  and  40. 

5.  16,  24,  and  48.  19.  32,  48,  and  72. 

6.  30,  40,  and  60.  20.  16,  22,  and  24. 

7.  2,  4,  8,  and  16.  21.  18,  28,  and  30. 

8.  14,  21,  and  28.  22.  12,  16,  and  20. 

9.  5,  8,  15,  and  18.  28.  33,  44,  and  55. 

10.  6,  9,  21,  and  24.  24.  27,  36,  and  42. 

11.  12,  20,  and  30.  25.  36,  45,  and  60. 

12.  6,  10,  30,  and  40.  26.  28,  35,  and  42. 
IS.  32,  48,  and  60.  27.  45,  55,  and  60. 
14.  24,  32,  and  40.  28.  60,  72,  and  84. 

CANCELLATION. 

38.  Cancellation  is  a  method  of  shortening  an  operation 
by  rejecting  equal  factors  from  both  dividend  and  divisor. 

39.  PRINCIPLES. — 1.  Canceling  or  rejecting  a  factor  from  a 
number,  divides  the  number  by  that  factor. 

2.  Dividing  both  dividend  and  divisor  by  the  same  number  does 
not  affect  the  value  of  the  quotient. 


CANCELLATION.  9 

Ex.  Divide  84  x  36  by  27  x  14. 

OPERATIONS.  ANALYSIS. — Indicate  the  oper- 

Or,  ations  to  be  performed  as  in  the 

flU  v  *£                      »  .  .  I  .     m  »    .  margin.     It  is  seen  by  inspection 
w               ,-,.     r  that  36  and  27  contain  the  com- 

6  4  rnon  factor  9  >  tnerefore  cancel  or 

reject  it  from  both,  retaining  the 

8  factors  4  and  3  respectively.  14 

and  84  contain  the  common  factor 

14;  therefore  reject  it,  retaining  the  factor  G  in  the  dividend.  [Since  cancel- 
lation is  a  process  of  division,  the  rejecting  of  14  does  not  destroy  it,  but 
divides  it,  leaving  1  as  a  quotient.  It  is  unnecessary  to  write  1  as  a  quotient, 
except  when  there  are  no  other  factors  in  the  dividend.]  3  is  a  common  fac- 
tor of  6  and  3 ;  therefore  reject  it  from  both,  retaining  the  factor  2  in  the 
dividend.  The  product  of  the  remaining  factors,  2  and  4,  is  the  required 
quotient. 

40.  RULE. — Indicate  the  operations  to  be  performed,  by 
writing  the  numbers  denoting  multiplication  above  a  hori- 
zontal line,  and  the  numbers  denoting  division  below.     The 
numbers  above  the  line  will  form  a  dividend,  and  the  num- 
bers below  a  divisor.     Cancel  or  reject  the  factors  common 
to  both  dividend  and  divisor.     The  product  of  the  remain- 
ing factors  of  the  dividend  divided  by  the  product  of  the 
remaining  factors  of  the  divisor  will  be  the  required  quo- 
tient. 

EXAMPLES. 

41.  1.  Divide  27  x  48  x  60  by  54  x  36  x  1-0. 
What  is  the  value  of  the  following  expressions  : 

40x36x42x18  24x30x54x35 

9x35x30x8  '  14x15x21x64* 

360_x28_x272<6  17  x 36  x 25  x  144 

*     25x42x18x12*  '     48x60x108x51' 

1760x175x6  1760  x  6  x  145 

4x9x100x10*  100x365 

1500  x  144  x  5  144x625x37x12 

~  365x100  288x375x185 

10.  Multiply  72  by  3  x  18,  divide  the  product  by  8  times  9, 
multiply  the  quotient  by  7  x  20,  divide  the  product  by  360;  mul- 
tiply the  quotient  by  6  times  8. 


10  PROPERTIES     OF    NUMBERS. 

11.  If  42  tons  of  coal  cost  $147,  what  will  16  tons  cost  ? 

12.  A  man  gave  9  pounds  of  butter  at  1 7  cents  a  pound  for 
3  gallons  of  molasses ;    how  much  was  the  molasses  worth  a 
gallon  ? 

13.  If  20  pounds  of  beef  cost  250  cents,  what  cost  75  pounds  ? 

14.  How  many  potatoes  at  65  cents  per  bushel  will  pay  for 
13  weeks'  board  at  $7.50  per  week  ? 

15.  A  merchant  bought  375  barrels  of  flour  at  $5.50  per  barrel, 
and  paid  in  cloth  at  $2.75  per  yard  ;    how  many  yards  did  it 
require  ? 

16.  How  many  pounds  of  coffee  at  27  cents  per  pound  should 
be  given  for  57  bushels  of  corn  at  63  cents  per  bushel  ? 

17.  Sold  28  bushels  of  apples  for  $21 ;  what  should  I  receive 
for  42  bushels  ? 

18.  How  many  cows  worth  $35  each  must  be  given  in  exchange 
for  84  tons  of  hay  at  $15  per  ton  ? 

19.  How  many  bushels  of  corn  at  52  cents  a  bushel  must  be 
exchanged  for  324  bushels  of  oats  at  39  cents  per  bushel  ? 

20.  If  430  bushels  of  wheat  are  obtained  from  sowing  7  bush- 
els, how  much  would  be  obtained  from  sowing  21  bushels  ? 

21.  What  should  be  paid  for  the  transportation  of  3600  pounds 
of  cheese  at  the  rate  of  47  cents  per  100  pounds  ? 

22.  What  must  be  paid  for  transporting  31600  pounds  of  iron 
at  $5  per  ton  of  2000  pounds  ? 

23.  What  will  7840  pounds  of  coal  cost,   at  $6  per  ton  of 
2240  pounds  ? 

24.  If  3  men  eat  7  pounds  of  meat  in  one  week,  how  much 
would  6  men  eat  in  4  weeks  ? 

25.  How  many  canisters,  each  holding  40  ounces,  can  be  filled 
from  3  chests  of  tea,  each  containing  55  pounds  of  16  ounces  ? 

26.  How  many  times  can  16  bottles,  each  holding  3  pints,  be 
filled  from  6  demijohns,  each  containing  10  gallons  of  8  pints 
each  ? 

27.  A  man  exchanged  275  barrels  of  potatoes,  each  containing 
3  bushels,  at  54  cents  per  bushel,  for  a  certain  number  of  pieces 
of  muslin  each  containing  45  yards,  at  11  cents  per  yard.     How 
many  yards  did  he  receive  ? 

28.  If  a  person  travel  24  hours  each  day  at  the  rate  of  45  miles 
an  hour,  how  many  days  would  it  require  to  pass  around  the 
globe,  a  distance  of  25000  miles  ? 


REVIEW    EXAMPLES.  11 


REVIEW     EXAMPLES. 

4:2.  1.  Write  in  figures  each  of  the  following  numbers,  add 
them,  and  express  in  words  (or  numerate)  their  sum  :  Forty-five 
thousand  and  forty-five ;  sixteen  thousand  three  hundred  and  sixty ; 
one  hundred  and  sixty-seven  thousand  ;  eight  hundred  and  fifty 
thousand  and  ninety-two  ;  nine  million  and  twenty-four. 

2.  Subtract  eight  hundred  and  fourteen  thousand  nine  hun- 
dred and  sixteen  from  four  million  and  nineteen  thousand. 

3.  Multiply  five  hundred  and  sixty  thousand  seven  hundred 
and  eight  by  eighteen  hundred  and  sixty. 

4.  A  quantity  of  merchandise  was  bought  for  $27618.75,  and 
sold  for  $32418.25.     What  was  the  gain  ? 

5.  What  is  the  sum  of  2817,  273,  30006,  97,  7285,  2700576, 
7000781,  27  ? 

6.  If  I  sell  goods  for  $23876,  and  gain  $5389,  what  did  the 
goods  cost  me  ? 

7.  What  is  the  sum  of  the  prime  numbers  from  20  to  50  ? 

Add  the  following  numbers  as  they  stand,  from  left  to  right, 
and  from  right  to  left.  [In  making  out  bills,  and  in  other  com- 
mercial operations,  a  great  deal  of  time  can  be  saved  by  adding  in 
this  manner,  without  re-arranging  the  numbers.  ] 

8.  17,  27,  36,  14,  43,  42,  65,  73,  81,  35. 

9.  137,  414,  528,  345,  678,  975,  864,  357,  121,  234. 

10.  67.16,  5.12,  3.75,  475,  38.42,  59.27,  38.75,  175.25. 

11.  2345,  16,  375,  4218,  376,  7,  8475,  247,  39. 

12.  1234.27,  348.25,  775,  7.16,  89.76,  374.12,  5673.56,  397.23. 

Find  the  difference  between  the  numbers  in  each  of  the  fol- 
lowing groups.  [In  all  of  these  cases  the  subtrahend  is-placed 
above  the  minuend,  the  purpose  being  to  give  the  student  practice 
in  subtracting  downward  rather  than  upward,  as  the  general  cus- 
tom is.  It  is  often  requisite  in  business  to  perform  the  work  in 
this  way,  and  the  accountant  should  practice  both  methods.] 

(13.)  V4.)  (15-)  (16.)  (17.) 

76534  19827  26347  72016  12345 

81279  84362  71356  99385  54321 


12  PROPERTIES     OF    NUMBERS. 

18.  One  factor  of  a  certain  number  is  217  and  the  other  5280  ; 
what  is  the  number? 

19.  Find  the  prime  factors  of  108108. 

W.  If  the  quotient  is  375  and  the  divisor  246,  what  is  the 
dividend  ? 

21.  If  the  product  of  two  factors  is  450072,  and  one  of  the 
factors  is  987,  what  is  the  other  factor  ? 

22.  What  is  the  sum  of  the  composite  numbers  from  60  to  90 
inclusive  ? 

23.  Divide   76432801  by  783.    Prove  that  your  solution  is 
correct. 

24..  A  clerk  receiving  a  salary  of  $1256,  pays  $468  a  year  for 
board,  $180  for  clothing,  and  $150  for  other  expenses.  "What 
amount  has  he  left  ? 

25.  What  is  the  least  number  that  can  be  exactly  divided  by 
each  of  the  following  numbers  :  24,  32,  80,  48,  and  90  ? 

26.  If  I  take  24889  from  the  sum  of  9872  and  24967,  divide 
the  remainder  by  50,  and  multiply  the  quotient  by  18,  what  is  the 
product  ? 

27.  If  160  acres  of  land  cost  $10720,  how  many  acres  can  be 
bought  for  $8844? 

28.  What  is  the  least  common  multiple  of  the  nine  digits  ? 

29.  If  75  head  of  cattle  cost  $2550,  what  will  59  head  cost  ? 
SO.  A  merchant  sold  426  barrels  of  flour  for  $2556,  which  was 

$639  more  than  he  gave  for  it.     What  did  it  cost  him  a  barrel  ? 

31.  What  is  the  greatest  number  that  will  exactly  divide  each 
of  the  following  numbers  :  246,  744,  and  522  ? 

32.  What  is  the  smallest  sum  of  money  with  which  horses  can 
be  bought  at  $96  each,  cows  at  $30  each,  or  sheep  at  $5  each,  using 
the  same  amount  in  each  case  ? 

33.  A  merchant  bought  387  yards  of  cloth  at  79  cts.  per  yard  ; 
he  sold  298  yards  at  $1.16  per  yard,  and  the  remainder  at  97  cts. 
per  yard  ;  how  much  did  he  gain  ? 

34.  Cash  on  hand  at  beginning  of  the  day,  $6492.75  ;  cash 
received,    $11456.75;   cash  paid  out,   $13285.26.     Required  the 
cash  balance  at  the  end  of  the  day. 

35.  Mr.  A  has  three  farms,  the  first  of  which  contains  158 
acres,  the  second  32  acres  less  than  the  first,  and  the  third  as 
many  as  the  other  two.    What  is  the  value  per  acre,  if  all  are 
worth  $26128  ? 


REVIEW    EXAMPLES.  13 

36.  There  are  five  bidders  to  supply  the  government  with  800 
tons  Lehigh,  500  tons  Cumberland,  and  700  tons  Baltimore  coal. 
A  offers  Lehigh  at  $6.29,  Cumberland  at  $4.38,  and  Baltimore  at 
$7.23.     B  offers  Lehigh  at  $6.80,  Cumberland  at  $4.12,  and  Balti- 
more at  $7.24.     C  offers  Lehigh  at  $6.40,  Cumberland  at  $4.45, 
and  Baltimore  at  $7.18.     D  offers  Lehigh  at  $6.17,  Cumberland  at 
$4.19,  Baltimore  at  $7.20.    E  offers  Lehigh  at  $6.50,  Cumberland 
at  $4.33,  and  Baltimore  at  $7.25.    Who  is  the  lowest  bidder  for  the 
whole  amount,  and  how  much  does  each  bid  amount  to  ? 

37.  A  drover  bought  a  number  of  cattle  for  $12204,  and  sold 
the  same  for  $13560,  by  which  he  gained  $4  per  head.     How  many 
cattle  were  purchased  ? 

38.  A  farmer  raised  in  one  year  512  bushels  of  wheat,  the  next 
year  twice  as  much  as  he  raised  the  first  year,  and  the  third  year 
four  times  as  much  as  he  did  the  second  year.     What  was  the 
value  of  the  three  crops  at  $1.65  per  bushel  ? 

39.  How  many  pounds  of  tea  at  78  cts.  per  pound  must  be 
given  for  375  bushels  of  wheat  at  $1.56  per  bushel  ? 

40.  Bought  75  tons  of  hay  at  $16  per  ton ;  gave  in  payment 
56  sheep  at  $3.75  each,  and  the  remainder  I  paid  in  butter  at 
33  cts.  per  pound.     How  many  pounds  of  butter  were  required  ? 

41.  Bought  225  acres  of  land  for  $12600,  and  sold  116  acres  at 
$65  per  acre,  and  the  remainder  at  cost ;  how  much  did  I  gain  ? 

42.  The  estimated  number  of  bushels  of  corn  produced  in  the 
United  States  in  1877  was  1,342,558,000,  the  total  value  of  crop 
was  $480,643,400,  and  the  total  area  of  crop  was  50,369,113  acres. 
What  was  the  average  value  per  bushel,  and  average  value  of  yield 
per  acre  ? 

43.  In  1878  there  were  39258  postmasters  in  the  United  States, 
and  their  total  salaries  were  $7,977,852 ;  what  was  the  average 
salary  paid  ? 

44.  July  1,  1866,  the  public  debt  of  the  United  States  was 
$2,773,236,173,  and  May  1,  1880,  $1,968,314,753;  what  was  the 
average  monthly  decrease  ? 

45.  A  sold  to  B  175  acres  of  land  at  $135  an  acre,  and  by  so 
doing  gained  $1925  ;  B  sold  the  land  at  a  loss  of  $1750.     What 
did  A  pay  per  acre,  and  what  was  B's  selling-price  per  acre  ? 

46.  A  merchant  sold  800  barrels  of  flour  for  $5867,  144  barrels 
of  which  he  sold  at  $7  per  barrel,  and  225  barrels  at  16.75.    At 
how  much  per  barrel  did  he  sell  the  remainder  ? 


FRACTIONS. 


DEFINITIONS. 

43.  A  Fraction  is  one  or  more  of  the  equal  parts  of  a  unit ; 
as  one-half  (J),  two-thirds  (f  ),  one-fourth  (J),  seven-eighths  ($). 

If  a  unit  be  divided  into  four  equal  parts,  each  part  is  called  a  fourth.  If 
one  of  these  parts  be  taken,  the  expression  will  be  one-fourth  (£; ;  if  three 
parts,  three-fourths  (f ),  etc. 

44.  The  greater  the  number  of  equal  parts  into  which  a  unit 
is  divided,  the  less  will  be  each  part ;  the  less  the  number  of  parts, 
the  greater  will  be  each  part. 

One-half  (-£)  is  greater  than  one-third  (£) ;  one-fourth  (|)  is  less  than  one- 
third  (i). 

45.  A  fraction  is  usually  expressed  by  two  numbers,  one 
written  above  the  other,  with  a  line  between.     Fractions  written 
in  this  form  are  usually  called  Common  Fractions. 

46.  The  number  below  the  line  is  called  the  Denominator, 
because  while  indicating  the  number  of  equal  parts  into  which 
the  unit  is  divided,  it  denominates  or  names  those  parts. 

47.  The  number  above  the  line  is  called  the  Numerator, 
because  it  shows  how  many  of  the  parts  are  taken  to  form  the 
fraction. 

48.  The  numerator  and  denominator,  taken  together,  are 
called  the  Terms  of  the  fraction. 

In  the  fraction  three-fourths  (f ),  3  and  4  are  the  terms ;  4  is  the  denomi- 
nator, and  shows  that  the  unit  is  divided  into  four  equal  parts,  called  fourths ; 
3  is  the  numerator,  and  shows  that  three  of  these  parts  are  taken  to  constitute 
the  fraction. 

49.  A  fraction  is  an  expression   of  unperformed  division. 
The  numerator  is  the  dividend,  the  denominator  is  the  divisor, 
and  the  value  of  the  fraction  is  the  quotient. 


DEFINITIONS.  15 

50.  A  Simple  Fraction  is  a  single  fraction,  both  of  whose 

terms  are  integers. 

51.  Simple  fractions  are  proper  or  improper. 

52.  A  Proper  Fraction  is  one  that  is  less  than  a  unit  ;  the 
numerator  being  less  than  the  denominator.     Thus,  £,  f,  and  -J 
are  proper  fractions. 

53.  An  Improper  Fraction  is  one  that  is  equal  to,  or 
greater  than  a  unit  ;  hence  the  numerator  must  be  equal  to,  or 
greater  than  the  denominator.     Thus,  f,  £,  -J,  and  ty-  are  im- 
proper fractions. 

54.  A  Mixed  Number  is  an  integer  and  a  fraction  united  ; 
as  24,  4J,  18$. 

55.  A  Compound  Fraction  is  a  fraction  of  a  fraction  ;  as 

i  of  |,  I  of  74,  |  of  |. 

56.  A  Complex  Fraction  is  one  whose  numerator  is  a 

}      105f     75J     3f     124 

fraction  or  mixed  number  ;    as    ~,    —  —  ^  ,    —£9   -f-,   ~-~- 

o         1/c         lo        o        15 

Q3 

The  expression  •£  indicates  division,  and  is  not  properly  a  fraction, 

D2 

A  unit  cannot  be  divided  into  5|  equal  parts. 

57.  PRINCIPLES.  —  1.  Multiplying  the  numerator  or  dividing 
the  denominator  by  a  number  multiplies  the  fraction  ly  that  number. 

2.  Dividing  the  numerator  or  multiplying  the  denominator  by  a 
number  divides  the  fraction  by  that  number. 

3.  Multiplying  or  dividing  both  numerator  and  denominator  by 
the  same  number  does  not  change  the  value  of  the  fraction. 

EXERCISES. 

58.  1.  Read  the  following  fractions,  and  copy  separately  : 
1,  the  simple  fractions  ;  2,  the  proper  fractions  ;  3,  the  improper 
fractions  ;  4,  the  mixed  numbers  ;  5,  the  compound  fractions  ; 
6,  the  complex  fractions  : 


H;   *i;  ¥;  A;  1;  ¥<>*«; 

;    i;    if;     ?f;    SJ;    46|;    ^;    ft;    -     ;    f;    |  of  f  . 


16  FRACTIONS. 

2.  Write  the  following  fractions:  three  fourths  ;  seven  eighths; 
nineteen  sixteenths ;  five,  and  one  half ;  one  hundred  and  three 
thirty-seconds ;    one  hundred,   and  three  thirty-seconds ;    forty- 
eight,  and  five  twelfths  ;  eleven  tenths  ;  nine  forty-fifths  ;  thirty- 
six  twenty-eighths ;  sixty-five  forty-eighths. 

3.  Write  the  following  fractions  :  eight  ninths ;  thirteen,  and 
two-thirds ;  sixteen  twenty-fourths ;   ten  tenths ;   fourteen,  and 
forty-six  hundredths  ;  nineteen  one  hundred  nineteenths  ;  thirty- 
six  four  hundred  thirty-seconds. 

REDUCTION. 

59.  Reduction  of  Fractions  is  the  changing  their  form 
without  changing  their  value. 

60.  A  fraction  is  reduced  to  lower  terms  when  the  numerator 
and  denominator  are  expressed  in  smaller  numbers. 

61.  A  fraction  is  in  its  lowest  terms  when  its  numerator  and 
denominator  have  no  common  divisor. 

62.  A  fraction  is  reduced  to  higher  terms  when  the  numerator 
and  denominator  are  expressed  in  larger  numbers. 

63.  To  reduce  a  fraction  to  its  lowest  terms. 

Ex.  Eeduce  -ffo  to  its  lowest  terms. 

OPERATION.  ANALYSIS. — Dividing  both  terms  of  the  fraction, 

•f/j  —  -J-f  =  f        TVir>  by  the  common  divisor,  6,  the  result  is  -|f ; 

dividing  both  terms  of  ^  by  the  common  divisor, 

7,  the  result  is  § .     Since  2  and  3  have  no  common  divisor,  the  fraction  is 
reduced  to  its  lowest  terms  (61). 

The  value  of  the  fraction  has  not  been  changed,  because  both  terms  have 
been  divided  by  the  same  number  (57,  3).  * 

The  same  result  is  often  more  readily  obtained  by  dividing  both  terms  by 
the  greatest  common  divisor. 

64.  EULE. — Divide  the  terms  of  the  fraction  by  any 
number  that  will  divide  both  without  a  remainder,  and 
continue  the  operation  -with  the  resulting  fractions  until 
they  have  no  common  divisor.     Or, 

Divide  the  terms  of  the  fraction  by  their  greatest  com- 
mon divisor. 


RED  UCTION. 

EXAMPLES. 

65.   Reduce  to  their  lowest  terms, 
1.     H.  9.     T%.  17.     -ffff.  25.     |ff. 

2.  «•        -*0.  «f.        is.  m-        00-  iff* 
£  if        ^.  i-Il        ^. 

6.     -ffg.  13.     iff}.  ^. 

&  T¥V.       ^-  Hi-        ^. 

15.     #&.  23. 


66.  To  reduce  a  fraction  to  higher  terms. 
Ex.    Reduce  f-  to  a  fraction  whose  denominator  is  32. 

OPERATION.  ANALYSIS.— The  fraction  f  is  reduced  to  thirty - 

32  -f-  4  —  8         seconds^  without  changing  its  value,   by  multiplying 
jl  —  24.  the  terms  by  the  number  that  will  cause  its  denomina- 

tor 4  to  become  32  (57,  3).     By  dividing  the  required 

denominator  32  by  the  given  denominator  4,  this  number  is  found  to  be  8. 
Multiplying  both  terms  of  f  by  8,  the  result  is  f $. 

67.  RULE. — Divide    the    required    denominator  by  the 
denominator  of  the  given  fraction,  and  multiply  both  terms 
of  the  given  fraction  by  the  quotient. 

EXAMPLES. 

68.  1.  Reduce  |-  to  48ths. 

2.  Change  -fe  to  an  equivalent  fraction  having  60  for  its 
denominator. 

3.  Reduce  f ,  |,  •&  each  to  48ths. 

4.  Reduce  -f,  •§,  -f-J  each  to  105ths. 

5.  Reduce  f|-,  f,  J-  each  to  56ths. 

6.  Reduce  T\,  -}J,  -Jf  each  to  96ths. 

7.  Reduce  -J,  f,  t3o  each  to  360ths. 

8.  Reduce  £},  f ,  fj-  each  to  72ds. 
P.  Reduce  |,  ff,  ^-f  each  to  108ths. 

^.  Reduce  f,  f,  J£  each  to  360ths. 


18  FRACTIONS. 

69.  To  reduce  two  or  more  fractions  to  equivalent 
fractions  having  their  least  common  denominator. 

70.  A  Common  Denominator  of  two  or  more  fractions  is 
a  denominator  to  which  they  can  all  be  reduced,  and  is  the  com- 
mon multiple  of  their  denominators. 

71.  The  Least  Common  Denominator  of  two  or  more 
fractions  is  the  least  denominator  to  which  they  can  be  reduced, 
and  is  the  least  common  multiple  of  their  denominators. 

Ex.    Reduce  •§,  f-,  |,  ^  to  equivalent  fractions  having  their 
least  common  denominator. 

OPERATION.  ANALYSIS. — The  least  common 

2    _   AQ.         2  )  $     4     6     10  multiple    of    the    denominators  is 

I  _  T|  ^ — • found  to  be  60  (3£>)'  which  we  take 

£od  as  the  least   common  denominator. 

By  Art.  67,  f  is  reduced  to  ft.    We 

A  =   |f  proceed   in  the  same  manner  with 

each  of  the  other  fractions.     The 

value  of  each  fraction  remains  unchanged,  since  both  terms  have  been  multi- 
plied by  the  same  number.  In  many  cases,  the  least  common  denominator 
can  be  readily  found  by  inspection. 

72.  RULE. — Find    the  least  common  multiple  of   the 
given  denominators  for  the  least  common    denominator, 
and  reduce  the  given  fractions  to  this  denominator. 


EXAMPLES. 

73.   Reduce  the  following  fractions  to  equivalent  fractions 
having  their  least  common  denominator  : 

i-    t  TV  TV  *    «,  ft  «•  9.    «,  -V3-,  v- 


A    tt>  A,  «•         r.    4,  «,  f  ^-    H,  H>  «- 

4    t  -VS  A-  A    «,  I,  «•  a    ft  «,  «- 

74.  To  reduce  an  integer  or  a  mixed  number  to  an 
improper  fraction. 

Ex.    In  18  units,  how  many  fourths  ? 


REDUCTION.  19 

OPERATION. 

18  ANALYSIS.— In  1  there  are  4  fourths  (£),  and  in  18, 

4  eighteen  times  4  fourths,  or  72  fourths  (^2-).    Hence, 

18  =  -7A 
72  fourths. 

Ex.    Eeduce  16 J  to  an  improper  fraction. 

OPERATION. 

16-J 
Q  ANALYSIS.— In  1  there  are  8  eighths  (f),  and  in  16, 

sixteen   times   8  eighths,  or  128  eighths  (if*).     128 
128  eighths.         eighths    and    7    eighths    are    135    eighths.      Hence, 
_7  eighths.       1«J  =  *&> 
135  eighths. 

75.  EULE. — Multiply  the  integer  by  the  required  denom- 
inator, and  to  the  product  add  the  numerator  of  the  frac- 
tion, and  under  the  result  write  the  denominator. 

NOTE. — When  the  numerator  of  the  fraction  is  a  small  number,  add  it 
mentally  to  the  product  of  the  integer  and  the  denominator. 


EXAMPLES. 

76.     1.  In  27,  how  many  ninths  ? 

2.  Eeduce  46  \  to  halves. 

3.  How  many  eighths  of  a  peck  in  37 -J  pecks  ? 

Eeduce  the  following  to  improper  fractions  : 

4.  37f;  19|;  208^.  9.     81f  ;  196£  ;  375|. 

5.  56| ;  49|;  182f  10.     116ft;  456T\  ;  87H- 

6.  375| ;  94TV  ;  46f.  11.     24t\  ;  179ft ;  1767 J. 

7.  44|;37A;19ft.  12.     87| ;  490^  ;  168ft. 

8.  12i;48&;45&.  18.     384| ;  161f;  175ff 


77.  To  reduce  an  improper  fraction  to  an  integer  or 
a  mixed  number. 

Ex.    Eeduce  -2^-  to  a  mixed  number. 

ANALYSIS. — 1  =  £  ;  hence  in  -2¥7,  there  are  as  many  units  as  4  fourths  are 
contained  times  in  27  fourths,  or  6f . 

78.  EULE. — Divide  the  numerator  by  the  denominator. 


20  FRACTIONS. 

EXAMPLES. 

79.     1.  Change  -4-1  to  a  mixed  number. 
2.  Eeduce  $£•  of  a  dollar  to  dollars. 

Reduce  to  integers  or  mixed  numbers  : 

£J£.  8. 

±4±.  9. 


ADDITION. 

80.  Addition  of  Fractions  is  the  process  of  finding  the 
sum  of  two  or  more  fractions. 

81.  PRINCIPLE.  —  In  order  thai  fractions  may  be  added,  they 
must  have  like  denominators  and  le  parts  of  like  units. 

Ex.    What  is  the  sum  of  ^,  -^  and  T^? 

OPERATION.  ANALYSIS.  —  As    these  frac- 

-fa  -\-  fy  +  iV  ~~  T!"  —-  %  ~  -^i        tions  have  a  common  denomina- 

tor, we  add  their  numerators, 

and  write  their  sum,  15,  over  the  common  denominator,  12.     j-f  =  1|,  the  re- 
quired result. 

Ex.    Add  f,  f,  and  |. 

OPERATION. 


ANALYSTS.  —  Reduce  the  given  fractions  to  equivalent  fractions  having  the 
least  common  denominator,  12  (72).     Then  proceed  as  in  previous  example. 

Ex.    Find  the  sum  of  29-fc  38},  17|,  and  42J. 


OPERATION. 


3g|.  is  ANALYSIS.  —  The  sum  of  the  fractions  is 

176.  14  If  =  lf>  which  added  to  the  sum  of  the  inte- 

®  gers,  gives  127|,  the  required  result. 

2f 


ADDITION.  21 

Ex.  How  many  yards  in  12  pieces  of  prints  containing  461, 
482,  512,  493,  441,  482,  471,  49,  473,  503,  481,  482  yards  respec- 
tively. 

OPERATION. 

451  471 

ANALYSIS.  —  The  sum  of  the  fourths  is  ^- 

5  12  473  =  5|-,  which  added  to  the  sum  of  the  integers 

49s  503  gives  580£,  the  total  number  of  yards. 

441  481 

482  4S2    5801. 

82.  RULE.  —  Reduce  the  given  fractions  to  equivalent 
fractions  having  the  least  common  denominator.     Write 
the  sum  of  the  numerators  over  the  coimnon  denominator, 
and  reduce  the  resulting  fraction  to  its  simplest  form. 

Wlien  there  are  mixed  numbers  or  integers,  add  the 
integers  and  fractions  separately,  and  then  add  the  results. 

EXAMPLES. 

83.  Add  the  following  : 

1-     fb  ii  A,  and  if.  5.     127A,  «,  l^i  and  f. 


2.  |,  f,  |,  and  -i.  6.     141^,  197$,  and  43^. 

3.  12J,  7|,  16A,  and  38f.          7.     75f,  |,  1028|,  and  «. 

and  17  8.          119      240      and 


9.  461,  483,  402,  49,  473,  and  462. 

10.  403,  411,  482,  441,  493,  482,  493,  491,  473,  483,  483,  and  491. 

11.  18|,  27i,  42|,  and  51|. 

12.  146J-,  If,  53^,  and  68J. 

18.  1172f,  19f,  440J,  and  6|. 
14.  A,  106A-,  37f,  and  7f 
^5.  175,  llfrft,  143J,  and  27f 
JTfi.  20|,  164f,  ff,  and  43|. 
77.  44i    16f,  29^,  and  13|. 

J&  311,  483,  621,  193,  272,  481,  and  373. 

19.  613,  481,  473,  48,  482,  491,  and  453. 

20.  19|,  444^,  737J,  and  385|. 


22  FRACTIONS. 


SUBTRACTION. 

84.  Subtraction  of  Fractions  is  the  process  of  finding 
the  difference  between  two  fractions. 

85.  PRINCIPLE.— /ft  order  that  fractions  may  be  subtracted, 
they  must  have  like  denominators  and  be  parts  of  like  units. 

Ex.    From  f  take  f. 

OPERATION.  ANALYSIS. — As  these  fractions  have  a  common 

•f-  —  f  —  f  =  J        denominator,  we  take  the  difference  of  the  numer- 
ators, and  place  it  over  the  common   denomina- 
tor,    f  =  £  is  the  result  required. 

Ex.    What  is  the  difference  between  J  and  f  ? 

OPERATION.  ANALYSIS. — Reduce  the  given  fractions 

9  —  8          j          to    equivalent    fractions  having  the  least 
^~        12        ~  T2"         common  denominator  (72).     Then  proceed 
as  in  the  previous  example. 

Ex.    From  176|  subtract  89}. 

OPERATION. 

176|.         s.  ANALYSIS,    f  from  §  we  cannot  take  ;  we  therefore 

8q  1  take  1  =  f  from  176,  leaving  175.      f  +  f  =  ^     V  ~  8 

— ±  =f.     175-89  =  86.    86  +  |  =  86|. 

set 

86.  RULE.— Reduce  the  given  fractions  to  equivalent 
fractions  having  the  least  common  denominator.  Write 
the  difference  of  the  numerators  over  the  common  denomi- 
nator, and  reduce  the  resulting  fraction  to  its  simplest 
form. 

When  there  are  mixed  numbers,  subtract  the  integers 
and  fractions  separately,  and  add  the  results. 


EXAMPLES, 
87.  Find  the  difference  between 

1.  j  and  |.  4.  2%  and  1-&.  7.  H  and  f. 

2.  |  and  -&.  5.  ^  and  T\.  8.  f  and  T4T. 

3.  f  and  ft-  6.  f  and  f .  9.  1  and  |f 


MULTIPLICATION.  23 

10.  17£  and  9}.  17.  116|  and  48f.  24-  "^  and  375^. 

11.  175J  and  86J.  18.  381|  and  17}.  86.  827J  and  737f. 

12.  138|  and  17±.  19.  157$  and  19}.  00.  919}  and  447^6. 
/&  149£  and  18f  20.  1183  and  48s.  27.  3761  and  2873. 

14.  416}  and  49}.        ^.  387|  and  116}.         0£.  445*  and  3183. 

15.  512}  and  53}.        22.  248^  and  129}.       29.  7373  and  438s. 
J0.  100    and  13}.        28.  764ft-  and  375}.       50.  6481  and  5263. 

MULTIPLICATION. 

88.  To  multiply  a  fraction  by  an  integer. 

89.  PKIKCIPLE.  —  Multiplying  the  numerator  or  dividing  the 
denominator  by  a  number  multiplies  the  value  of  the  fraction  by 
that  number  (57,  1). 

Ex.    What  will  4  pounds  of  tea  cost  @  $}  a  pound  ? 

OPERATIONS.  ANALYSIS.  —  If  1  pound  costs  $|, 

3.       A.  -     Z_*_f  _  28  __  qi         4  pounds  will  cost  4  times  $£,  or 

~~$~~  6*         $-2/->  equal  to  $3£.    Hence,  4  pounds 

of  tea  @$£  will  cost  $3|. 

Or>  To  multiply  f  by  4,  multiply  the 

»        A  7  .      _  QI         numerator  7  by  4,  or  divide  the  de- 

~  8~^4  "  *        nominator  8  by  4  ;  either  operation 

will  give  3|,  the  required  product 

Or>  (Prin.). 

%  X  f  =  I  =  3£  By  cancellation  (38),  the  opera- 

2  tion  is  shortened,  and  the  result  is 

obtained  in  its  lowest  terms. 

Multiplying  the  numerator,  as  in  the  first  operation,  increases  the  num- 
ber of  parts,  their  size  remaining  the  same  ;  dividing  the  denominator  multi- 
plies the  fraction  by  increasing  the  size  of  the  parts,  their  number  remaining 
the  same. 

Ex.    Multiply  123}  by  9. 


OPERATION. 


ANALYSIS.—  Multiply  the  fraction  f  and  the  integer  123 
9  separately,  and  add  the  products.     In  practice,  when  possible, 

TT         add  the  products  mentally  ;  e.g.,  9  times  f  are  \7-,  equal  to  6f. 
*         Write  the  f.    9  times  3  are  27,  and  6  are  33.    Write  the  3,  and 

proceed  as  in  simple  numbers. 
1113} 


24  FRACTIONS. 

Ex.    Multiply  227}  by  175. 

OPERATIONS.  ANALYSIS. — As  in  preceding  ex- 

227}         Or,  227}  ample. 

175  175  Or,  by  aliquot  parts,  when  the 

A  \  KOK  or/i  fractions   are  fourths,   eighths,  etc., 

/  the  fractions  generally  used  in  com- 

1314-  ^t  mercial  operations. 

1135 

1589 

£  of  175  =  87J. 


9O.  RULE. — Multiply  the  numerator  or  divide  the  de- 
nominator of  the  fraction  by  the  integer. 

When  the  multiplicand  is  a  mixed  number,  multiply 
the  fraction  and  integer  separately f  and  add  the  results. 


EXAMPLES. 

91.    1.  Find  the  cost  of  20  yards  of  silk  at  f-J  a  yard. 

2.  How  much  grain  in  12  bins,  each  containing  76  J  bushels  ? 

3.  If  1  man  earns  $J  in  1  day,  how  much  will  16  men  earn  in 
26  days? 

4.  If  a  ton  of  hay  cost  816},  how  much  will  22  tons  cost? 

5.  Required  the  cost  of  60  yards  of  muslin  at  35$  cents  a  yard  ? 

Multiply 


*•  A  by  7. 

77.  412f  by  47. 

0&  234J  by  318. 

7.  «by8. 

18.  148?  by  40. 

05.  678f  by  427. 

fttfty* 

JT0.  4124  by  89. 

80.  625}  by  516. 

9.  110J.  by  ia 

20.  775£  by  65. 

81.  71  8  J  by  542. 

10.  117}  by  16. 

21.  119A  by  20. 

,?0.  275|  by  287. 

11.  248£  by  3. 

#&•  772f  by  17. 

88.  813|  by  319. 

12.  146$  by  3. 

£3.  338|  by  30. 

54.  444J  by  412. 

13.  197^  by  7. 

24.  550$  by  27. 

85.  555£  by  875. 

14.  420^  by  8. 

25.  643}  by  121. 

86.  817}  by  416. 

15.  384|  by  12. 

26.  875|  by  234. 

57.  913}  by  375. 

16.  375£  by  48. 

07.  91  6J-  by  275. 

88.  787}  by  525. 

UNJVtK&l  j  T 

OF 


MULTIPLICATIO  N. 


25 


92.  To  multiply  an  integer  by  a  fraction,  or  to  find 
a,  fractional  part  of  an  integer. 

93.  PRINCIPLE. — Multiplying  by  a  fraction  is  taking  such 
part  of  the  multiplicand  as  the  fraction  is  of  a  unit. 

Ex.    If  1  ton  of  hay  cost  $18,  what  will  j  of  a  ton  cost  ? 


OPERATIONS. 

Or,  Or, 

18 


4)18 

3 

13* 

ANALYSIS.— If  1  ton  cost  $18,  £  of  a  ton  will  cost  £  of  $18.  £  of  $18  is 
3  times  ±  of  $18.  %  of  $18  is  $4|  (taking  £  is  the  same  as  dividing  by  4),  and 
3  times  $4|  is  $13£. 

Or,  £  of  $18  is  £  of  3  times  $18.     3  times  $18  is  $54.     {  of  $54  is  $13|. 

Ex.    Find  the  product  of  175  and  8f. 


ANALYSIS.— Multiply  by  the  frac- 
tion f  and  by  the  integer  8  separately, 
and  add  the  products. 


OPERATIONS. 

175        Or, 

_8J 
4)525 

175 

H 

43J 
3 

131J 
1400 
15314 

131J 
1400 

1531J 
Ex.    Multiply  275  by  47|, 


FIRST 
OPERATION. 


SECOND 
OPERATION. 


THIRD 
OPERATION. 


275 
J7| 
8  )  825 

275 
47| 

275 
_47| 
68J 
34* 
1925 
1100 

34$ 
3 

103£ 
1925 
1100 

103i 
1925 
1100 

130284 

13028J- 

13028-J 


ANALYSIS.  —  For  the  first  and 
second  operations,  as  in  the  pre- 
ceding examples. 

When  the  fractions  are 
fourths,  eighths,  etc.,  multiply 
by  means  of  aliquot  parts. 


i  of  275  =  68|. 
of  275,  or  £  of  68f  =  34|. 


26  FRACTIONS. 

94.  RULE.  —  Multiply  ~by  the  numerator  of  the  fraction., 
and  divide  the  product  by  the  denominator.     Or, 

Divide  by  the  denominator  of  the  fraction  and  multi- 
ply the  quotient  by  the  numerator. 

When  the  multiplier  is  a  mixed  number,  multiply  by 
the  fraction  and  integer  separately,  and  add  the  results. 

EXAMPLES. 

95.  1.  Find  the  cost  of  8f  yds.  of  ribbon  at  25  cts.  a  yard. 

2.  What  is  the  cost  of  42^  pounds  of  butter  at  26  cts.  a  pound. 
8.  Required  the  value  of  48-J  yards  of  flannel  at  75  cts.  a  yard. 

Multiply 

4.  84  by  f  .  10.  216  by  14f  .  16.  780  by  64f 

5.  126  by  f  11.  375  by  24f  17.  512  by  37f 

6.  49  by  |.  12.  375  by  22f  .  18.  611  by  87J. 

7.  128  by  9J,  1&  146  by  28f.  19.  625  by  92|. 

8.  156  by  8f  14.  184  by  16f  00.  937  by  75|. 

9.  187  by  lOf.  15.  110  by  41-}.  07.  575  by  81|. 

96.  To  multiply  a  fraction  by  a  fraction.* 

Ex.    At  If  a  pound,  what  will  |  of  a  pound  of  tea  cost  ? 

OPERATION  . 

3  v  7  __  si  __    7  ANALYSIS.  —  If  1  pound  cost  $J,  f  of  a  pound 

will  cost  f  of  $£.     f  of  $£  is  3  times  \  of  $£, 
Or>       }  X  i  =  -ft        i  of  $|  is  $^f  and  3  times  |£  is  $|  -J,  or  $TV 


Ex.    What  is  the  value  of  8  x  8$  x  T\  x  -^  ? 

2                  OPERATION  ANALYSIS.—  Reduce  the  inte- 

^.         5  ger  8  and  the  mixed  number  8£ 

f  X  ^  X  ^  X  ^¥  =  ^  =  3-J-  to  improper  fractions,  and  mul- 

^          x  tiply  as  in  the  preceding  example. 

97.  RULE.  —  Reduce  integers  and  jnixed  numbers  to  im- 
proper fractions. 

Cancel  all  factors  common  to  the  numerators  and  de- 
nominators. 


*  The  practical  methods  of  multiplying  one  mixed  number  by  another  are  given  under 
Art.  1O8. 


DIVISION.  27 

Multiply  the  remaining  numerators  together  for  the 
numerator,  and  the  remaining  denominators  for  the  de- 
nominator. 

EXAMPLES. 

98.  Find  the  product  of 

1.  |  and  -f.              5.  |  and  ^.  9.  £,  13J,  and  f 

&  f  and  f .              £.   6,  3J,  and  f.  J0.  26},  f  and  |. 

8.  |  and  -&.             7.  5f,  f,  and  fj.  11.  f,  j,  and  16f 

4.  |  and  J^.            A  124,  lOf,  and  ^.  72.  13$,  fc  and  -£. 

Reduce  the  following  compound  fractions  (55)  to  simple  ones. 
The  word  "  of"  is  equivalent  to  the  sign  x . 

13.  i  of  f  of  }.  17.  |  of  |  of  18.  21.  |  of  JJ  of  |f. 

14.  |  of  3|  of  f .  #.  |  of  llf  of  f  #0.  |  of  f  of  -I  of  |. 

15.  |  of  |  of  7f  ^P.  Jf  of  f|.  23.  }  of  12J  of  6|. 
75.  f  of  |  of  5f  «0.  A  of  |  of  ^.  24.  |  of  J|  of  4}. 

Find  the  value  of  the  following  expressions  : 

25.  |  of  1728.  30.  (\  +  T%)  x  (f  +  T5i)- 

*0.  I  x  375.  31.  (f  -  |)  x  «  +  J). 

07.  -i  times  864.  82.  (&  -f  f )  x  (-ft  -  *)• 

£?.  f  of  75  x  f  of  16f .  S3.  37J  times  f  of  ^ 

^P.  -i  x  f  of  ^  x  f .  54.  |  of  |  by  f  of  |. 


DIVISION. 

99.  To  divide  a  fraction  by  an  integer. 

100.  PRINCIPLE. — Dividing  the  numerator  or  multiplying 
the  denominator  ~by  a  number  divides  the  value  of  the  fraction  by 
that  number  (57,  2). 


23  FRACTIONS. 

Ex.  What  cost  1  pound  of  tea,  if  5  pounds  cost  $3J? 

OPERATIONS.  ANALYSIS. — If    5    pounds   cost 

10-1-5         2  $31,   1   pound  will  cost  £  of  $3J, 

¥-5-5=      -3—-*  Op$|. 

To  divide  V-  (3D  *>y  5,  divide 

n      10        *  -       10      10  2         the  numerator  10  by  5,  or  multiply 

JT>  TT  "*•  fi    -  3~x  5  ~  the    denominator    3    by    5  ;   either 

g  operation  will  give  f,  the  required 

Or    >£  X  i  =  f  quotient  (Prin.). 

Dividing  the  numerator,  as  in 

the  first  operation,  decreases  the  number  of  parts,  their  size  remaining  the 
same  ;  multiplying  the  denominator  divides  the  fraction  by  decreasing  the 
size  of  the  parts,  their  number  remaining  the  same. 

Ex.    Divide  867J  by  4. 

OPERATION.  ANALYSIS. — Dividing  as  in  simple 

4  )  867J          3f  =  ¥  numbers,  4  is  contained  in  867f,  216 

~21  fii&       Xfi.  _i-  4  14  times  and  a  remainder  of  3f .    3|  equals 

~  "  \5-,  which  divided  by  4  is  }§. 


101.  RULE. — Divide    the    numerator    or  multiply  the 
denominator  of  the  fraction  ~by  the  integer. 

When  the  dividend  is  a    mixed  number,  divide  the 
integer  and  the  fraction  separately,  and  add  the  results. 

EXAMPLES. 

102.  Divide 

1.  |  by  6.  11.  6371  by  9.  21.  5316|  by  4. 

2.  |  by  3.  12.  875.fr  by  12.  00.   7144£  by  5. 

3.  |  by  6.  IS.  1716|  by  8.  23.  1729J  by  3. 

4.  A  by  4-  ^  1729i  by 3-         %  1749i  by 9- 

5.  ^  by  4.  75.  2418|  by  5.  25.  8763£  by  6. 

6.  16|by5.  16.  3516f  by  5.  ^.  7385|  by  8. 

7.  172J  by  3.  17.  2428|  by  3.  27.  4255£  by  9. 

8.  875fby6.  18.  6375|  by  4.  28.  7134|  by  7. 
•9.  935 J  by  8.  19.  42871  by  2.  M-  9727^  by  12. 
10.  729Jby9.  20.  3281|  by  8.  30.  6345|  by  16. 


DIVISION.  29 

103.  To  divide  by  a  fraction. 

104.  The  Reciprocal  of  a  number  is  1  divided  by  that 
number.     Thus,  the  reciprocal  of  4  is  1  divided  by  4,  or  J. 

The  Reciprocal  of  a  Fraction  is  1  divided  by  that  fraction. 

105.  PRINCIPLE.     1  divided  by  a  fraction  is  the  fraction  in- 
verted. 

Thus,  1  divided  by  f  is  f.  This  principle  may  be  demonstrated  as  fol- 
lows :  In  1  there  are  4  fourths.  1  fourth  is  contained  in  4  fourths  4  times. 
Since  f  is  3  times  j,  f  is  contained  in  1  ^  as  many  times  as  £.  Hence,  f  is 
contained  in  1  ^  of  4  times,  or  f  times. 

The  reciprocal  of  a  fraction  is  the  fraction  inverted. 

Ex.    At  8f  a  yard,  how  many  yards  of  cloth  can  be  bought 

for  $5  ? 

OPERATIONS.  ANALYSIS. — Since  1    yard    cost 

5  _t_  3  — .  2_o.  _i_  3.  — .  gs.  $|,  as  many  yards  can  be  bought  for 

$5  as  $|  is  contained  times  in  $5. 
Or,   5  -7-  f  =  f  X  |  =  :  -2/  :  -  6|      5  is  equal  to  ^  and  3  fourths  is  con- 

tained  in  20  fourths  6|  times. 

Or,  $|  is  contained  in  $1  f  times  (Prin.)t  and  in  $5,  5  times  |  or  ^°-,  equal 
to  6f  times. 

Ex.  At  $|  a  yard,  how  many  yards  of  cloth  can  be  bought 
for  $|  ? 

OPERATIONS.  ANALYSIS.— Since  1  yard 

f  -r-  |  =  U  -T-  A  =  It  cost  $|,  as  many  yards  can  be 

n  _  5   v  4  --  ^  —  1 1         bought  for  $|  as  $|  is  con- 

tained times  in  $|.     f  is  equal 
»  to  T^,  and  |  is  equal  to  If. 

Jr>      f   •    f  '=  <  f  -  -  V"  :      Af         T\  is  contained  in  ^  1£  times. 

Or,  $|  is  contained  in  $1 
|  times  (Prin.),  and  in  $|,  f  times  f  or  f  f,  equal  to  1£  times. 

Ex.    If  6|  yards  of  cloth  cost  $5,  what  will  1  yard  cost  ? 

OPERATIONS.  ANALYSIS.     6|  yards  are 

5  -f-  -2/  :  =  (5  -*-  20)  X  3  =  f         equal  to  -\°-  yards.     Since  y 

Or       5  —  £o  —  s   v    3^  _  IB  _  a        yards  cost  $5»  i  of  a  yard 

K  *F'  will  cost  ^  of  $5  or  $1,  and 

Or,      5  -v-  -2/  =  f  X  A  =  }  f  or  1  yard  will  cost  3  times 

4  $1-  or  $f. 

Or,  the  price  per  yard  equals  the  cost,  divided  by  the  quantity  as  an  ab- 
stract number.  5  divided  by  %n-  equals  5  times  1  divided  by  -2/,  or  5  times  ^ 
(Prin.),  equal  to  f . 


30  FRACTIONS. 

Ex.    Divide  2195J-  by  175f. 

OPERATION. 

175 1  )  2195f  ANALYSIS. — Reduce  both  divisor  and  divi- 

6  6  dend  to  improper  fractions,  and  divide  as  in 


1054  )  13175  (  121  preceding  example. 

Or,  multiplying  both  divisor  and  dividend 

by  the  same  number  does  not  affect  the  quo- 

2635  tient.    Multiply  both  divisor  and  dividend  by 

QIAO  6,  the  least  common  denominator,  and  divide 

/41U5  . 

as  m  simple  numbers. 

527 

—    2 


1054 

106.  RULE. — Reduce  the  divisor  and  dividend  to  equiv- 
alent fractions  having  a  common  denominator,  and  divide 
the  numerator  of  the  dividend  by  the  numerator  of  the 
divisor.     Or, 

Invert  the  terms  of  the  divisor  and  proceed  as  in  multi- 
plication. 

In  dividing  mixed  numbers,  multiply  both  divisor  and 
dividend  by  the  least  common  denominator,  and  divide  as 
in  simple  numbers. 

EXAMPLES. 

107.  Divide 

1.  1  by  |.  U.  73  by  8*.  W.  920  by  73|. 

2.  16  by  f  15.  45  by  7f .  28.  720  by  43$. 

3.  28  by  f .  16.  8J  by  3}.  29.   700  by  37$, 

4.  49  by  f  17.  6|  by  3J.  SO.  560  by  26}. 

5.  88  by  f.  18.  4f  by  3f.  SI.  682 $  by  45  J. 

6.  J  by  -f.  19.  7$  by  8$.  88.  847£  by  89}. 

7.  f  by  f.  W.  9J  by  18$.  S3.  984*  by  753. 

8.  ^  by  j.  81.  875  by  33J.  &£.  862s  by  183. 

9.  T\  by  |.  88.  625  by  83$.  S5.  7311  by  56*. 
m  f  by  J.  83.  516  by  34f.  55.  431  i  by  18f. 
11.  28  by  4$.  84.  917  by  43f.  57.   983$  by  29$. 
18.  33  by  3|.  05.  864  by  86|.  S8.  504|  by  36|. 
IS.  64  by  5f.  05.  702  by  30f  S9.  583$  by  43 J. 


DIVISION. 


31 


Find  the  value  of  the  following  complex  fractions  (56)  and 
expressions  of  division : 

5A.    4I.    24f  fof4       40.31 

r'     ~9~'    35'   "36"  «*  fo 


'    5f-3 


?i.  ?l. 

40'    13' 


5*.  i.  A 
H'  V    *' 


175J  — 


68|--MJ 

f    38f  — 


—  186  J' 


8f 


1O8.  To  multiply  mixed  numbers  together.* 

Ex.  What  cost  101 6 J  pounds  of  cotton,  at  12$-  cents  per 
pound  ? 

Instead  of  reducing  the  mixed  numbers  to  improper  fractions,  use  the  fol- 
lowing methods.  The  second  method  (by  aliquot  parts)  is  preferable,  and  is 
well  adapted  to  commercial  operations,  in  which  the  fractions  are  usually 
halves,  fourths,  eighths,  etc. 

In  business  transactions,  it  is  customary  to  omit  the  fraction  in  the  result, 
if  it  is  less  than  |,  and  to  add  1  to  the  cents  if  it  is  more  than  -|.  Unless  other- 
wise stated,  the  exact  answers  will  be  given  to  examples.  . 


FIRST  OPERATION. 

1016$ 


8  )  3049^ 


12198 
125.79T3¥ 

SECOND  OPERATION. 

1016J 


ANALYSIS. — Multiply  1016 1  by  the  fraction  |  by 
multiplying  by  the  numerator  3  and  dividing  by  the  de- 
nominator 8  (92) ;  theij  multiply  1016|  by  the  integer 
12  (88),  and  add  the  results. 


12198 


ANALYSIS,  f  =  £  +  £.  Multiply  101 6|  by  £  by  di- 
viding by  4.  Multiply  1016|  by  $  by  taking  £  of  the 
254£,  the  product  by  £.  Multiply  1016'-  by  12  (88), 
and  add  the  results. 


*  The  multiplication  of  mixed  numbers  is  purposely  put  in  this  connection,  as  it  appro- 
priately comes  here,  a  knowledge  of  division  of  fractions  being  a  prerequisite  to  a  fair 
understanding  of  the  process. 


32 


FRACTIONS, 


EXAMPLES. 


109.   (1.) 


837f 
150794 

15917J 


(2.) 


16754 


Or, 


837}  [prod,  by  4] 

418J[prod.byi(4of4)] 

1734 
11725 
6700 
5025 


5826554 


16754 
347J 
4 )  50264 
1256| 
1734 
11725 
6700 
5025 
5826554 


864}     [4+i] 
126}     [4  +  i] 
432|-     [prod,  by  4] 
108A  [Pi'od.  byi( 
63       [126  xi] 


Or, 


5184 
10368 
109498f4 

Multiply  in  like  manner, 

4.  8754  by  84 ; 

5.  737J  by  104; 

6.  512}  by  74 ; 

7.  449-f  by  16}  ; 

8.  1612}.  by  134  ; 

9.  2437f  by  164  5 


by  12J 
by  274 
by  36| 
by  42| 
by  12{ 


5  by  26}. 
;  by  44|. 

by  64}. 

by  45}. 

by  185}. 


126| 
8  )  4323| 


944  4)378 

•  5184 

10368 

109498J4 


REVIEW     EXAMPLES. 

11O.     1.  Eeduce  fff  to  its  lowest  terms 

2.  Eeduce  |  to  forty-eighths. 

3.  Eeduce  72 7|  to  an  improper  fraction. 

4.  Eeduce  J-3%51  to  a  mixed  number. 

5.  Add  17-4,  37},  18|,  49},  13|,  and 


REVIEW    EXAMPLES.  33 

6.  From  1728£  take  865£. 

7.  Multiply  i  X  3|  x  A  x  T3<r  X  16f 

8.  Multiply  1727}  by  175. 

9.  Multiply  1727  by  175|. 

10.  Divide  1J  by  -f^. 

11.  Divide  1736  by  144f. 

12.  Divide  5779|  by  275f. 

18.  Divide  12346J  by  7 ;    by  35. 

14.  What  is  the  cost  of  1583  pounds  sugar  @  11J  cts.  per 
pound  ? 

jf5.  Add  |  of  |  of  4fr,  |,  136f ,  and  2X 

.?£.  A  merchant  sold*a  quantity  of  goods  for  $7344,  which  was 
|  of  the  cost.     What  was  the  loss  ? 

17.  Required  the  value  of  2993  pounds  of  sugar  @  9f  cts.  per 
pound  ? 

18.  If  |  of  a  ship  is  worth  $42430£,  what  is  the  value  of  the 
whole  ? 

19.  Bought  47|  yards  of  cloth  at  $4£  per  yard,  and  paid  for  it 
in  wheat  at  $2J  per  bushel ;  how  many  bushels  were  required  ? 

20.  Find  the  value  of  3  Iff  pounds  snuff  @  72  cts.  per  pound. 

21.  The  less  of  two  numbers  is  777f  and  their  difference 
11 7| ;  what  is  the  greater  number  ? 

22.  A  and  B  together  have  $1728 ;  if  A's  money  is  equal  to  J- 
of  B's,  how  much  have  each  ? 

23.  A  merchant  having  2146f  yards  of  cloth,  sold  -|  of  it  at 
$1|  a  yard,  and  the  remainder  at  $&J-  a  yard  ;  how  much  did  he 
receive  ? 

24.  A  number  being  increased  by  f  of  itself,  the  sum  is  546  ; 
what  is  the  number  ? 

25.  A  man  had  $5280  ;  he  bought  goods  with  f  of  it,  and  then 
lent  J-  of  the  balance  to  a  friend ;  how  much  had  he  left  ? 

26.  Find  the  selling  price  of  goods  sold  at  a  profit  of  $75, 
being  f  of  the  cost. 

27.  Mr.  A  bought  117f  acres  of  land  at  one  time,  and  87 1  at 
another ;  after  selling  110^  acres,  how  much  remained  ? 

28.  If  8}  tons  of  coal  cost  $30 f,  what  will  27|  tons  cost  ? 
How  many  tons  can  be  bought  for  $127J  ? 


34  FRACTIONS. 

29.  A  man  paid  $1145|  for  a  horse  and  carriage.     What  was 
the  value  of  each,  the  carriage  being  valued  at  f  as  much  as  the 
horse  ? 

30.  If  |  of  a  farm  is  valued  at  $2253},  what  is  the  value  of  f 
of  it? 

31.  What  is  the  value  of  2102 l  yards  prints  at  72  cents  per 
yard  ? 

82,  What  number  must  be  taken  from  96},  and  the  remainder 
multiplied  by  16f,  that  the  product  shall  be  770£? 

88.  What  is  the  value  of  1642  yards  muslin  at  5j  cents  per 
yard? 

3Jf.  If  7  barrels  of  oil  contain  313}  gallons,  how  many  gallons 
will  2}  barrels  contain  ? 

35.  An  executor  collects  $12724.84.     He  pays  out   $4096.48 
and  the  residue  he  disburses  to  the  widow  and  her  four  children 
as  follows  :  The  widow  receives  a  third  part,  and  the  remainder 
is  divided  equally  among  the  children.     What  was  the  share  of 
each? 

36.  What  number  increased  by  f  of  itself  will  produce  245  6-J-  ? 

37.  Find  the  selling-price  of  goods,  bought  at  $144,  and  sold 
at  -J-  above  cost. 

88.  A  invests  f  of  his  capital  in  real  estate,  and  has  $1725 
remaining  ;  what  is  his  capital  ? 

39.  Bought  a  barrel  of  sugar  containing  218  Ibs.,  at  8}  cents 
per  pound.     During  the  sale,  it  dried  away  -fa.     Did  I  gain  or 
lose,  and  how  much,  by  selling  it  at  9}  cents  per  pound  ? 

40.  Multiply  2375}  by  8}  •"  by  10}. 

41.  Multiply  1727}  by  18}  ;  by  107|. 

42.  Multiply  377}  by  16} ;  by  37}. 
4S.  Multiply  875}  by  22};  by  9|. 

44-  A  merchant  sold  12J  yards  of  silk  to  one  customer,  21}  to 
another,  20f  to  another,  and  28}  to  another;  at  $2f  per  yard, 
how  many  dollars  did  he  receive  ? 

45.  An  army  loses  -f^  of  its  number  in  battle  and  has  16042 
remaining ;  how  many  did  it  originally  contain  ? 

46.  What  is  the  cost  of  34  pieces  prints,  containing  16042 
yards,  at  51  cents  per  yard  ? 

47.  What  is  the  value  of  12  pieces  prints  containing  48,  481, 
482,  48,  492,  483,  48,  493,  49s,  483,  492,  483  yards  respectively  at 
43  cents  per  yard  ? 


REVIEW    EXAMPLES. 


35 


48.  A  merchant  purchased  29  pieces  prints  containing  48 3, 
482,  412,  482,  4S3,  47,  49,  49*,  521,  573,  483,  482,  38,  482,  482, 
482,  473,  482,  48,   51,  48,  441,  512,  48,  423,  462,  48,  482,  483 
yards  respectively ;  what  was  the  cost  at  52  cents  per  yard  ? 

49.  There  are  5280  feet  in  one  mile,  and  16 £  feet  in  one  rod ; 
how  many  rods  in  one  mile  ? 

50.  A  can  do  a  certain  piece  of  work  in  10  days,  and  B  can 
do  it  in  15  days  ;  how  long  will  it  take  them  both  to  do  it  ? 

51.  A  market-woman  bought  120  oranges  at  the  rate  of  5  for 
2  cents,  and  sold  J  of  them  at  the  rate  of  3  for  1  cent,  and  the 
remainder  at  the  rate  of  2  for  1  cent.     Did  she  gain  or  lose,  and 
how  much  ? 

52.  What  is  the  duty  on  22375  pounds  sugar,  at  2^f  cts.  per 
pound  ? 

53.  A  farmer  sold  1276£f  bushels  oats  at  44  cts.  per  bushel, 
876|f  bushels  corn  at  52j-  cts.,  and  3381ff  bushels  wheat  at  $1.32  ; 
how  much  did  he  receive  ? 

5Jf.  How  many  bushels  of  corn  at  54J  cts.  per  bushel  must  a 
farmer  exchange  for  62  yards  of  sheeting  at  8f  cts.  per  yard,  and 
31  yards  broadcloth  at  $1. 75  per  yard  ? 

55.  What  is  the  value  of  45 3  yards  damask  at  77 2  cts.  per 
yard? 

56.  The  salary  of  the  President  of  the  United  States  is  $50000 
per  year  ;  how  much  is  that  per  day  ? 

57.  1T4^-  pounds  of  beef  and  1T^-  pounds  of  flour  are  allowed  to 
ration  ;  how  much  will  617  rations  cost,  if  the  price  of  beef  is 
11|  cts.  per  pound,  and  of  flour  3J  cts.  per  pound  ? 

58.  What  is  the  value  of  36385  pounds  of  corn  at  48 J  cents  per 
bushel,  each  bushel  containing  56  pounds  ? 

59.  Foreign  immigration  since  1870,  by  fiscal  years  : 


Years. 

Number. 

Years. 

Number. 

Years. 

Number. 

1870    .  .  . 

356  303 

1874  .     . 

260  814 

1878  

138,469 

1871 

346  938 

1875 

191  231 

1879  

177,826 

1872  

437,750 

1876  

237,991 

1880  

457,257 

1873  

422,545 

1877  

141  857 

1881  

669  439 

According  to  the  above  table,  what  was  the  average  immigra- 
tion per  year  ?    What  per  month  ? 


DECIMALS. 


DEFINITIONS. 

111.  A  Decimal  (from  the  Latin  decem,  ten)  Fraction  is 
a  fraction  whose  denominator  is  1  followed  by  one  or  more  ciphers  ; 

aS    TO?    'TWO'     1000' 

112.  Decimal  fractions  arise  from  dividing  a  unit  into  10 
equal  parts,  and  then  dividing  these  parts  into  10  other  equal 
parts,  and  so  on. 

Thus,  if  a  unit  be  divided  into  10  equal  parts,  each  part  is  called  a  tenth. 
If  a  unit  be  divided  into  100  equal  parts,  or  1  tenth  into  10  equal  parts,  the 
parts  are  called  hundredths.  If  a  unit  be  divided  into  1000  equal  parts,  or 
1  hundredth  into  10  equal  parts,  the  parts  are  called  thousandths. 

113.  All  the  rules,  principles,  operations,  etc.,  of  common 
fractions  may  be  applied  to   decimal   fractions.     Since   decimal 
fractions  increase  and  decrease  uniformly  according  to  the  scale 
of  ten,  a  more  simple  notation,  similar  to  that  of  integers,  has 
been  devised  for  them. 

A  hundred  is  written  100  ;  a  tenth  part  of  a  hundred  (ten)  is  written  10, 
the  1  being  written  one  place  to  the  right ;  a  tenth  part  of  one  ten  (one  unit) 
is  written  1,  the  1  being  written  one  place  to  the  right ;  in  like  manner,  a  tenth 
part  of  one  unit  (one-tenth)  is  written  .1,  the  1  being  written  one  place  to  the 
right ;  the  tenth  part  of  one-tenth  (one  hundredth)  is  written  .01,  the  1  being 
written  one  place  to  the  right,  etc.,  etc. 

Decimal  fractions,  like  integers,  decrease  from  left  to  right  in  a  tenfold 
ratio,  and  increase  from  right  to  left  in  the  same  ratio. 

114.  In  the  decimal  notation,  the  numerator  only  is  written, 
the  denominator  being  indicated  by  the  position  of  a  point  ( . ) 
called  the  decimal  point.    The  decimal  point  separates  the  inte- 
gral from  the  fractional  part. 


DEFINITIONS.  37 

115.  The  denominator  of  a  decimal  fraction  is  understood, 
and  is  1  with  as  many  ciphers  annexed  as  there  are  figures  in  the 
decimal  ;  thus, 

Form  of  Form  of 

common  fraction.         decimal  fraction. 

-fa    is  written    .7    and  is  read    seven  tenths. 

«          .08       "        "       eight  hundredths. 
«          .016     "        "       sixteen  thousandths. 

Hereafter,  the  first  form,  that  of  the  common  fraction,  will  be  called  a 
fraction,  and  the  second,  that  of  the  decimal  notation,  a  decimal. 

116.  The  first  place  to  the  right  of  the  point  is  called  tenths, 
the  second  place  hundredths,  the  third  place  thousandths,  and 
so  on. 

117.  The  relation  between  integers  and  decimals  is  shown  in 
the  following 

NUMEKATION   TABLE. 


4 

<&•  3 


• 


. 

a  .j    ^3     i  ft    ' 

§  9     5    J     J 

PH  S  I     °     4     J     ^ 

-  «  1  1  1  1  1 


II  1 1  I  1 1  I  1     *  1 i  * 


2436. 807, 5  93  „  689460582 


Orders  of  Integers.  Orders  of  Decimals. 

118.  In  the  above  table,  observe  that  the  first  place  to  the 
left  of  units  is  called  tens,  and  the  first  place  to  the  right,  tenths  ; 
the  second  place  to  the  left  of  units  is  called  hundreds,  and  the 
second  place  to  the  right,  hundredths,  etc.     Hence  the  number 
of  any  order  or  place  of  the  decimal,  counting  from  the  point,  or 
from  units'  place,  is  the  same  as  the  number  of  ciphers  in  the 
denominator  of  the  decimal. 

119.  A  Complex  Decimal  has  a  fraction  in  its  right-hand 
place. 

Thus,  .16f  ( -jj}  is  a  complex  decimal,  and  is  read  16|  hundredths,  the 
fraction  not  being  counted  as  a  decimal  place. 


38  DECIMALS. 

12O.   PRINCIPLES.  —  1.  Annexing  ciphers  to  a  decimal  does  not 
alter  its  value. 

Annexing  a  cipher  multiplies  both  the  numerator  and  denominator  by  10, 
and  hence  does  not  alter  the  value  of  the  decimal  (57,  3).     Thus,  .7  (T%)  = 


2.  Each  removal  of  the  decimal  point  one  place  to  the  right 
multiplies  the  value  of  the  decimal  by  10. 

Removing  the  point  one  place  to  the  right  does  not  change  the  numerator, 
but  divides  the  denominator  by  10,  and  hence  multiplies  the  value  of  the  deci- 
mal (57,  1).  Thus,  .072  (dfa)  becomes  .72  (flfc)  ;  ^  =  T£fir  x  10. 


3.  Each  removal  of  the  decimal  point  one  place  to  the  left  divides 
the  value  of  the  decimal  ly  10. 

Removing  the  point  one  place  to  the  left  does  not  change  the  numerator, 
but  multiplies  the  denominator  by  10,  and  hence  divides  the  value  of  the  frac- 
tion by  10  (57,  2).  Thus,  .72  (rffr)  becomes  .072  (T^f0)  ;  Tflfo  =  jfo  +  10. 


NUMERATION    OF    DECIMALS. 

RULE. — Read  the  decimal  as  if  it  were  an  integer, 
and  give  it  the  name  of  its  right-hand  order. 

EXERCISES. 

122.  Write  in  words,  or  read  orally  the  following  numbers  : 

1.  .6.  8.  17.6.  15.  375.18J. 

&  .008.  9.  8.029.  16.  19.0033$. 

8.  .27.  10.  24.000488.  17.  6.148f. 

4.  .0375.  11.  400.000088.  18.  648.6|. 

5.  .0108.  12.  76.7071.  19.  347.18005. 

6.  .775.  13.  3000.0045.  W.  808.008. 

7.  .1007.  14.  .3045.  21.  600.06. 

NOTATION    OF    DECIMALS. 

123.  Write  in  the  form  of  a  decimal,  sixty-four  thousandths. 
ANALYSIS.— Since  there  are  only  two  figures  in  the  numerator  64,  and  the 

right-hand  figure  of  the  decimal  must  occupy  the  third  decimal  place  to  ex- 
press thousandths,  it  is  necessary  to  prefix  a  cipher  to  bring  the  right-hand 
figure  into  its  proper  place.  Therefore  write  point,  naught,  six,  four  (.064)  in 
the  order  named. 


NOTATION.  39 

124.  RULE. — Prefix  the   decimal    point,  and  decimal 
ciphers  if  necessary,  to  the  numerator  ivritten  as  an  integer, 
so  that  the  right-hand  figure  will  occupy  the  order  named. 

NOTE. — Before  writing,  determine  mentally  the  place  of  the  right-hand 
figure  and  the  number  of  ciphers  required.  Write  in  all  cases  from  left  to 
right. 

EXERCISES. 

125.  1-  What  is  the  name  of  the  third  decimal  order  ?    The 
sixth  ?    The  first  ?    The  fourth  ? 

2.  How  many  decimal  places  are  required  to  express  hun- 
dredths  ?  Millionths  ?  Ten-thousandths  ?  Tenths  ?  Hundred- 
millionths  ? 

S.  How  many  ciphers  must  be  written  after  the  decimal  point 
in  writing  375  millionths  ?  27  hundredths  ?  875  thousandths  ? 
446  ten-millionths  ?  37  ten- thousandths  ? 

4.  Write  the  following  as  decimals,  so  that  the  decimal-points 
stand  in  the  same  vertical  line:  8  tenths;  16  hundredths;  175 
thousandths ;  1804  millionths ;   56  ten-thousandths ;   3004  ten- 
millionths  ;  1728  ten-thousandths. 

NOTE.— In  the  following  exercises,  the  comma  is  used  to  separate  the  inte- 
gral and  decimal  parts. 

5.  Seventeen,  and  seventy-five  hundredths. 

6.  Twenty-six,  and  twenty-six  thousandths. 

7.  Two  hundred  and  forty-six  ten-millionths. 

8.  Two  hundred,  and  forty-six  ten-millionths. 

9.  Three  hundred  and  seventy-five,  and  eighteen   hundred- 
thousandths. 

10.  Eight  thousand,  and  sixty-five  ten- thousandths. 

11.  Eight  thousand  and  sixty-five  ten-thousandths. 

-*'v>  TO>  ~nn5>  I"~n5>  ^l^Toinr?   i  o  o  o  o  • 

13.  16-,%,  19-rffo,  345^, 

14.  28rdHhr,  3W,  Sf&rJWr 

15.  170^^,  IGOOOnflyU  38^, 
16. 


40  DECIMALS. 

REDUCTION. 

126.  To  reduce  a  fraction  to  a  decimal. 

Ex.    Eeduce  f  to  a  decimal. 

OPERATION. 

4.  \  3^00  ANALYSIS,     £  equals  £  of  3  units.     3  units  equal  300 

hundredths.     £  of  300  hundredths  equal  75  hundredths. 

•75 

127.  RULE. — Annex  decimal  ciphers  to  the  numerator, 
and  divide  by  the  denominator,  pointing  off  as  many  deci- 
mal places  in  the  quotient  as  there  are  ciphers  annexed. 

128.  A  fraction  in  its  lowest  terms  can  be  reduced  to  a  pure 
decimal  only  when  its  denominator  contains  no  prime  factors  but 
2  and  5.    If  the  denominator  or  divisor  contain  any  prime  factor 
other  than  2  and  5,  the  division  will  not  end.     The  decimals  thus 
produced  are  called  Interminate  or  Repeating  Decimals, 
and  the  figures  repeated,  Bepetends. 

When  a  fraction  is  in  its  lowest  terms,  its  numerator  and  denominator 
have  no  common  factors  (61).  Annexing  ciphers  to  the  numerator  intro- 
duces the  factors  2  and  5  only ;  hence,  if  the  denominator  is  an  exact  divisor 
of  the  numerator  with  the  ciphers  annexed,  it  must  contain  these  prime  fac- 
tors and  none  others. 

EXAMPLES, 

129.  Reduce  to  equivalent  decimals : 

1.  f  4.  *•  7.  H-  10.  A-  IS.  16f 

2.  f.  5.  -&.  8.  f.  11.  f  14.  27if. 

3.  f.  6.  ||.  9.  f  .12.  f  15.  36ff. 

130.  To  reduce  a  decimal  to  a  fraction. 

Ex.    Reduce  .075  to  an  equivalent  fraction. 

ANALYSIS. — A  decimal  is  changed  to  a 

OPERATION.  fraction  by  writing  its  denominator,  and  omit- 

.1)75  =  Yoinr  —•  4*V  ting  the  decimal  point  and  prefixed  ciphers. 


ADDITION.  41 

Ex.    Change  .83  J  to  a  simple  fraction. 

OPERATION.  ANALYSIS.  —  Reduce  the 

-33  =  H*  =  *  —  fraction  »  to  a 


simple  fraction  by  multi- 
plying both  terms  by  the  denominator  3.     (57,  3.) 

131.   RULE.  —  Omit  the  decimal  point,  supply  the  proper 
denominator,  and  reduce  the  fraction  to  its  lowest  terms. 


EXAMPLES. 
132.   Reduce  to  equivalent  fractions  : 


1.  .25.  8.  .128.  15.  .33£.  88.  .44f. 

8.  .75.  9.  .00144.  70.  .41|.  85.  .142857-?-. 

S.  .375.  70.  .512.  17.  .066|.  0J.  .0833J. 

4.  .625.  11.  .5625.  7S.  .37£.  25.  28.0375. 

5.  .875.  70.  .1875.  19.  .104f  00.  107.166-f. 

6.  .125.  75.  .12f  )80.  .097f.  87.  175.096. 

7.  .016.  14.  .16f.  07.  .0053f  0*.  6.0175. 

ADDITION. 

133.  Since  decimals,  like  integers,  increase  and  decrease  uni- 
formly according  to  a  scale  of  ten,  with  the  exception  of  placing 
the  decimal  point  in  the  result  (usually  called  pointing  off),  they 
may  be  added,  subtracted,  multiplied,  and  divided  in  the  same 
manner  as  integers. 

Ex.   What  is  the  sum  of  28.7,  175.28,  .037,  25.0045,  and  4.08  ? 

OPERATION. 

ANALYSIS.— Write  the  numbers  so  that  units  of  the 
175.28  same  order  stand  in  the  same  column. 

%03^  If  the  decimal  points  are  in  the  same  vertical  line, 

25  0045         tentns  will  necessarily  be  under  tenths,  hundredths  under 
hundredths,  etc.    Add  as  in  integers,  and  place  the  point 
_Z___        in  the  result  directly  under  the  points  of  the  numbers. 
233.1015 


42  DECIMALS. 

Ex.    Add  .6,  .37|,  16.048$,  8.1234f,  and  24.125. 

OPERATION.  ANALYSIS. — Reduce  the  complex  deci 

•6  —        .6  mals  as  far  as  the  decimal  places  extend 

.37}        =        .3775  in  tlie  other  numbers.     Since  the  fractions 

16  048 l      =   1604834-  now  express  parts  of  the  same  fractional 

'  9oL  unit>  they  may  be  added. 

In  practice,  the  fractions  may  be  re- 

24.125        =   24.125  jected  if  the  decimals  are    carried    one 

49.2742A3-        place,  at  least,  farther  than  accuracy  is  re- 
quired. 

134.  RULE. —  Write  the  numbers  so  that  their  decimal 
points  are  in  the  same  vertical  line.  Add  as  in  integers, 
and  place  the  decimal  point  in  the  result  directly  under 
the  points  in  the  numbers  added. 


EXAMPLES. 

135.  1-  Add  ninety-seven  hundredths ;  three  hundred  and 
forty-seven  thousandths ;  sixteen,  and  seventy-five  hundred-thou- 
sandths; four  hundred  and  seventy-five,  and  two  thousand  and 
thirty-seven  millionths. 

2.  Add  four,  and  eighty-one  thousandths  ;  thirty-seven,  and 
two  hundred  and  one  ten-thousandths  ;  seven  thousand  and  eight 
hundred-thousandths ;  seven  thousand,  and  eight  hundred-thou- 
sandths ;  nineteen  hundredths ;  three  hundred  and  sixty-four, 
and  nine  tenths;  and  fifty-six,  and  fifty-four  thousandths. 

3.  Add  three  hundred  and  seventy-five,  and  eight  hundredths ; 
eighteen  thousandths  ;    ninety-six,  and  eighty-four  hundredths  ; 
four,  and  four  tenths ;  and  eight  hundred  and  seven  ten-millionths. 

4.  What  is  the  sum  of  18  hundredths ;  716  hundred- thou- 
sandths ;  6342  millionths ;   11567  ten-millionths ;    625  ten-thou- 
sandths ;  9  tenths  ;  99  hundredths  ;  and  512  thousandths  ? 

5.  Add    81.86;    12.593;    4.004;    18.00129;    .443;     400.043; 
.12875;  175.00175;  17.3008;  9000.0016;  and  .9016. 

6.  Required,  the  sum  of    99   ten-thousandths ;    157£   thou- 
sandths ;  789}  millionths  ;  6  tenths ;  18}  hundredths ;  1728  ten- 
millionths  ;  and  88  hundredths. 

7.  Add  $1728.64;    $0.37£ ;    $18.44£;    $10.18};    $6.25;    and 
$0.16^. 


SUBTRACTION.  43 

8.  What  is  the  sum  of  $12.37|;  $144.18  J;  $6.62£;  $175.06J ; 
$40.17$;  and  $398? 

9.  Add   .1264|;    12.875;    187.25;   9.1414f ;    .12;    5.7604^; 
and  .0008f. 

10.  Add  .26J;  4.18|;  .0017f;  .008644;  .04f;  17.387^;  and 
.0102075. 

SUBTRACTION. 

136.  Ex.  From  12.75  subtract  8.125. 

OPERATION.  ANALYSIS. — Write  the  subtrahend  under  the  minuend  so 

12.75  that  units  of  the  same  order  stand  in  the  same  column.     Sub- 

8.125         tract  as  in  integers,  and  place  the  point  in  the  result  directly 

~         under  the  points  of  the  numbers. 

4:.o/c£>  j^  ag  jn  thjs  exampie)  the  minuend  has  not  as  many  deci- 

mal places  as  the  subtrahend,  suppose  decimal  ciphers  to  be 
annexed  until  the  right-hand  figures  are  of  the  same  order.    (12O.) 
Reduce  complex  decimals  as  in  addition  (133). 

137.  EULE. —  Write  the  numbers  so  that  their  decimal 
points  are  in  the  same  vertical  line.     Subtract  as  in  inte- 
gers, and  place  the  point  in  the  remainder  directly  under 
the  points  in  the  minuend  and  subtrahend. 


EXAMPLES. 

138.  L  From  four,  and  sixty-five  thousandths,  subtract 
eight  hundred  and  forty-seven  ten-thousandths. 

2.  From  twenty-seven  hundredths  take  twenty-nine  hundred- 
thousandths. 

8.  From  nine  thousand,  and  thirty-four  ten-thousandths,  sub- 
tract nine  thousand  and  thirty-four  ten-thousandths. 

Find  the  difference  between 

4.  8.3644  and  7.8996.  12.  17.864|  and  16.94. 

5.  17.4586  and  .785.  IS.  144. 43^  and  113.3875. 

6.  1.010101  and  .999999.  14.  54.3 7|  and  .98f. 

7.  $173.46  and  $87.29.  15.  117.48J  and  49.43f 

8.  3  and  .873845.  16.  448.987^  and  389.28f 

9.  17.24£  and  18.973J.  17.  5556.&J-  and  44.48. 

10.  $510.60  and  $389.45f  18.  968.44f  and  37.386|. 

11.  $1728  and  $.06f.  19.  49.45£  and  48.9876f 


44  DECIMALS. 

MULTIPLICATION. 

139.  Ex.  Multiply  .144  by  .12. 

OPERATION.  ANALYSIS. — For  convenience,  write  the  right-hand  figures 

144  °^  *ke  ^ac^ors  in  *ne  same  vertical  line. 

12  .144  x  .12  =  TVir4(r  x  fifa  =  iWA-     Multiply  the  numera- 

tors of  the  two  factors  for  the  numerator  of  the  product,  as 
.01728  in  multiplication  of  fractions.     In  the  above  multiplication 

of  fractions,  it  will  be  observed  that  the  number  of  ciphers 
in  the  denominator  of  the  product  equals  the  sum  of  the  ciphers  in  the  de- 
nominators of  the  two  factors.  Since  each  cipher  represents  a  decimal  place, 
the  product  should  have  as  many  decimal  places  as  both  factors. 

If  the  number  of  figures  in  the  product  is  less  than  the  number  of  decimal 
places  in  the  two  factors,  supply  the  deficiency  by  prefixing  ciphers. 

140.  EULE. — Multiply  as  in  integers,  and  from  the 
right  point  off  as  many  decimal  places  in  the  product  as 
there  are  decimal  places  in  the  two  factors. 

NOTE.— -To  multiply  a  decimal  by  10,  100,  1000,  etc.,  remove  the  decimal 
point  as  many  places  to  the  right  as  there  are  ciphers  in  the  multiplier, 
annexing  ciphers  to  the  multiplicand,  if  necessary. 

EXAMPLES. 

141.  1.    Multiply  three  hundred  and  forty-four  ten-thou- 
sandths by  twelve  thousandths. 

2.  Multiply  one  hundred  and  ninety-two  thousandths  by  four, 
and  nineteen  hundredths. 

5.  What  is  sixteen  hundredths  of  six  hundred  and  thirty-two 
millionths  ? 

4.  What  is  five  hundredths  of  $864.32  ?     Of  3645.75  francs? 

6.  What  is  .058$  of  784.65  ?     Of  943.25  ? 

6.  What  is  .99  x  1.106  x  .25  ?     4.105  x  .625  x  .512  ? 

Multiply  Multiply 

7.  8.716  by  .39  ;  by  .047.       12.  17.28  by  .016| ;  by  2.55$. 

8.  .00865  by  .625  ;  by  97.75.     18.  64.32$  by  1.44| ;  by  .06$. 

9.  .00128  by  8756.8  ;  by  7.865.    14.  86.75  by  1.33$ ;  by  5.76f 

10.  387.25  by  .0147$ ;  by  .087f    15.  5.78  by  .0885 ;  by  .66f . 

11.  58.625  by  .488f  ;  by  .375.     16.  237.5  by  .345$  ;  by  4.468^. 


DIVISION.  45 

17.  Of  1728,  what  is  .75  ?    .33£  ?    .25?    .125?     .20?    .625? 

18.  Multiply  (2.108  -f  .0074)  by  (12.684  —  .465). 

19.  Multiply  .01837  by  1000  ;  .00145  by  100000 ;  .6874  by  100  ; 
5.375  by  10  ;  17.056  by  10000.    What  is  the  sum  of  the  products  ? 

20.  What  is  the  square  of  .0364  ?     Of  20.75  ?    Of  45.25  ? 

21.  What  is  the  cube  of  8.045  ?    Of  .0875  ?     Of  67.375  ? 


DIVISION. 

142.  Ex.  Divide  .01728  by  1.44. 

OPERATION.  ANALYSIS.— Dividing  as  in  integers,  witli- 

1.44  )  .01728  (  .012          out  reference  to  the  decimal  points  and  pre- 
144  fixed  ciphers,  the  quotient  is  12.     Since  the 
OOQ  dividend  is  the  product  of  the  divisor  and  quo- 
tient, it  must  contain  as  many  decimal  places 
as  both  of  them. 

0  Hence  the  number  of  decimal  places  in  the 

quotient  must  equal  the  number  in  the  divi- 
dend less  the  number  in  the  divisor. 

If,  as  in  this  example,  the  number  of  figures  in  the  quotient  is  less  than 
the  number  of  decimal  places  to  be  pointed  off,  supply  the  deficiency  by  pre- 
fixing ciphers. 

143.  RULE. — Divide  as  in  integers,  and  point  off  from 
the  right  of  the  quotient  as  many  decimal  places  as  the 
number  in  the  dividend  exceed  those  in  the  divisor, 

NOTES. — 1.  If  the  divisor  contains  more  decimal  places  than  the  dividend, 
before  dividing  make  them  equal  by  annexing  ciphers  to  the  dividend.  If 
necessary  to  continue  the  division,  more  ciphers  may  be  added. 

2.  If,  after  dividing  all  the  figures  of  the  dividend,  there  is  a  remainder, 
the  division  may  be  continued  by  annexing  ciphers  (12O).    The  ciphers  thus 
annexed  must  be  regarded  as  decimal  places  of  the  dividend. 

3.  To  divide  a  decimal  by  10,  100,  1000,  etc.,  remove  the  decimal  point  as 
many  places  to  the  left  as  there  are  ciphers  in  the  divisor,  prefixing  ciphers  to 
the  dividend,  if  necessary. 

EXAMPLES. 

144.  1.  Divide  three  thousand  four  hundred  and  fifty-six 
hundred-thousandths  by  seventy-two  hundredths. 

2.  Divide  six,  and  twenty-five  hundredths  by  twenty-five  thou- 
sandths. 


46  DECIMALS. 

Divide 

3.  35.88  by  .345 ;  by  4.16.  8.  .0648  by  .00425  ;  by  .0288. 

4.  .89958  by  .47  ;  by  .319.  9.  .31752  by  .648 ;  by  .00384. 

5.  12.6  by  14.4 ;  by  .125.  10.  .1898  by  .33$  ;  by  .0048f . 

6.  96.3  by  .20  ;  by  .25.  11.  85.2451  by  4.56| ;  by  8.27f 

7.  5.27  by  1.24;  by  .85.  12.  45.367  by  .016f ;  by  l.OSOf 

13.  Divide  17.28  by  .20  ;  by  .25  ;  by  .33| ;  by  .125  ;  by  .66|. 

14.  321  is  .178£  of  what  number  ? 

15.  186  is  five  hundredths  of  what  number  ? 

16.  What  must  37.375  be  multiplied  by  to  produce  448.5  ? 

17.  What  must  631.25  be  divided  by  to  produce  250  ? 

18.  Divide  176.824  by  100  ;  876.35  by  1000  ;  17380.5  by  10000  ; 
2886.57  by  10  ;  375  by  1000000.     Find  the  sum  of  the  quotients. 

19.  $12.52  is  how  many  hundredths  of  $375.60  ? 

20.  $273.60  is  how  many  thousandths  of  $1728  ? 

REVIEW     EXAMPLES. 

145.     1.  Add  16  hundredths,  137  millionths,  48  ten-thou- 
sandths, and  2016  ten-millionths. 

2.  Add  16.07,  240.127f,  6.04},  27.1234. 

3.  Reduce  -ff  to  a  decimal. 

4.  Reduce  .083^  to  a  fraction. 

5.  From  175  take  16.083J. 

6.  From  375.16f  take  1 98.888 -f. 

7.  Change  .8375  to  a  fraction. 

8.  Multiply  117.084  by  7.37|. 

9.  Divide  43.75  by  .0125. 

10.  Divide  .06f  by  1.66f. 

11.  1.75  is  I  of  what  number? 

12.  What  is  §  of  $175.75  ? 

13.  What  is  .33  of  187.5  ? 
14-  What  is  .33J  times  1728  ? 

15.  $3.75  is  how  many  hundredths  of  $75  ? 

16.  $86.40  is  how  many  hundredths  of  $2592  ? 

17.  16.56  is '.05  of  what  number? 

18.  What  will  17280  bricks  cost  at  $3.25  per  M.  ? 

10.  If  278  barrels  of  pork  cost  $4378.50,  what  is  the  cost  of 
100  barrels  ? 


REVIEW    EXAMPLES.  47 

20.  What  cost  12456  feet  of  plank  at  $8.75  per  M.  ? 

21.  What  is  the  value  of  5  bbls.  sugar,  containing  312,  304, 
301,  305,  304  pounds  respectively,  at  9-f  cents  per  pound  ? 

22.  A  miller  wishes  to  purchase  an  equal  quantity  of  wheat, 
corn,  and  rye  ;  he  pays  for  wheat  $2.22-}-  a  bushel ;  for  corn,  98  \ 
cents  a  bushel;  and  for  rye  $1.16-|  a  bushel.     How  many  bushels 
of  each  can  he  buy  for  $92776.50  ? 

28.  Bought  280  cords  of  hard  wood,  at  $6.75,  and  790  cords  of 
soft  wood,  at  $3.62£  per  cord.  Also,  750  bushels  of  corn,  at  62  J 
cents,  and  925  bushels  of  oats,  at  37£  cents  per  bushel.  What  was 
paid  for  the  whole,  and  what  was  the  average  price  of  wood  per 
cord,  and  of  grain  per  bushel  ? 

24.  Bought  on  contract  350  reams  of  foolscap  paper,  at  $3.83-}- 
per  ream,  45|-  reams  of  which  were  returned  as  unsuitable,  and 
275  reams  of  letter,  at  $2.67-}-  per  ream,  37-|  reams  of  which  were 
rejected.    How  much  was  paid  for  the  remainder  ? 

25.  A    merchant    paid    for    merchandise    during    the    year 
$137618.75,  and  sold  merchandise  to  the  amount  of  $146347.87. 
What  was  the  gain,  if  the  net  market  value  of  the  merchandise 
remaining  unsold  was  $24378  ? 

26.  A  quartermaster  has  $8345  on  hand,  and  receives  $4379.62 
from  each  of  six  sales  of  property ;   he  turns  over  to  quarter- 
master A  $2875.28,  and  pays  $120  for  corn.     Upon  being  relieved 
from  duty,  he  turns  over  to  quartermaster  B  one-third  of  the 
residue,  and  divides  the  remainder  equally  among  three  others, 
C,  D,  and  E.    What  was  paid  over  to  each  ? 

27.  Merchandise  on  hand,  Jan.l,  1879,  $46312.85;  merchan- 
dise sold  during  the  year,  $317829.32  ;  merchandise  purchased  in 
the  same  time,  $301449.72 ;  merchandise  on  hand,  Dec.  31,  1879, 
$61378.12.     What  was  the  net  gain  or  loss  ? 

28.  A  farmer  sold  land  for  $22.50  an  acre,  as  follows  :  to  A, 
98f  acres ;  to  B,  |  of  the  number  sold  to  A  ;  and  to  C?  £  the 
number  sold  to  A  and  B  both.     How  much  land  was  sold,  how 
much  did  B  and  C  each  receive,  and  what  was  the  amount  realized  ? 

29.  What  are  the  prime  factors  of  2791  ? 

30.  At  $28.75  per  thousand,  how  many  feet  of  lumber  should 
be  given  for  2816  pounds  of  sugar  at  7T3g-  cts.  per  pound  ? 

31.  Mr.  A  offered  to  sell  his  horse  for  -^  more  than  it  cost 
him,  but  afterward  sold  it  for  $504,  which  was  TV  less  than  his 
first  asking  price.     How  much  did  his  horse  cost  him  ? 


48  DECIMALS. 

32.  In  England,  during  the  year  1875,  there  were  147,730,313 
tons  of  bituminous  coal  produced,  535,845  persons  employed,  and 
1244  lives  lost.  How  many  tons  of  coal  were  produced  to  each 
person  employed,  how  many  tons  to  each  life  lost,  and  how  many 
persons  were  employed  per  life  lost  ? 

S3.  In  the  anthracite  coal  mines  of  Pennsylvania,  during  the 
year  1875,  there  were  22,000,000  tons  of  coal  produced,  69,589 
persons  employed,  and  238  lives  lost.  How  many  tons  of  coal 
were  produced  to  each  employe,  how  many  to  each  life  lost,  and 
how  many  persons  were  employed  to  each  life  lost  ? 

34.  In  the  Lehigh  district  of  Pennsylvania,  in  1878,  there  were 
3,956,588  tons  of  coal  produced,  and  51,492  kegs  of  powder  used. 
How  many  tons  of  coal  were  produced  per  pound  of  powder  used, 
each  keg  containing  25  pounds  ? 

35.  A  man  bequeaths  -J  of  his  property  to  his  wife,  £  to  his 
son,  -J  to  his  daughter,  and  the  remainder,  which  is  $36375,  to 
charitable  institutions.     What  is  the  amount  bequeathed  to  each, 
and  the  total  amount  ? 

36.  If  a  person  traveling  3-J  miles  per  hour  completes  a  jour- 
ney in  16J-  hours,  what  time  would  it  require  if  he  traveled  4J 
miles  per  hour  ? 

37.  If  I  purchase  two  building  lots  for  $3750  each,  and  sell  one 
for  |  more  than  it  cost,  and  the  other  for  .  33-J  less,  what  is  the 
gain  or  loss  on  the  two  lots  ? 

38.  A  speculator  sells  two  farms  for  $6000  each ;  how  much 
does  he  gain  or  lose,  if  he  sells  one  for  .20  more  than  it  cost,  and 
the  other  for  -£  less  than  it  cost? 

39.  A  gentleman  after  spending  -J-  of  all  his  money,  and  {  of 
the  remainder,  had  $177.50  remaining  ;  how  much  had  he  at  first  ? 

40.  A  merchant  bought  100  yards  of  cloth  at  $3.62J  per  yard, 
and  87J  yards  at  $4.12£  per  yard.     At  what  average  price  per  yard 
should  he  sell  the  whole,  to  realize  a  profit  equal  to  ^  of  the  cost  ? 

Jt.1.  If  31J  bushels  of  corn  cost  $17.50,  how  many  bushels  can 
be  bought  for  $616  ? 

1$.  *In  1864  there  were  33908  miles  of  railroad  in  operation  in 
the  United  States,  and  in  1878,  81841  miles.  What  was  the  aver- 
age annual  increase  of  mileage  ? 

*  This  is  exclusive  of  sidings.  Mr.  Poor,  from  whose  Manual  the  above  was  taken,  esti- 
mates that  there  are  19,500  miles  of  railroad  in  double,  treble,  and  quadruple  tracks,  sidings, 
etc.,  making  the  total  length  of  single  track  equal  to  101,341  miles  in  1878. 


DENOMINATE     NUMBERS. 


DEFINITIONS. 

146.  A   Denominate  Number  is  a  concrete  number  (7), 
and  may  be  either  simple  or  compound. 

147.  A  Simple  Denominate  Number  refers  to  units  of 
the  same  name  and  value  ;  as  7  inches,  4  pounds. 

148.  A  Compound  Denominate  Number  refers  to  units 
of  different  names,  but  of  the  same  nature  ;  as  3  feet  C  inches,  4 
pounds  8  ounces. 

149.  Denominate  numbers  are  used  to  express  divisions  of 
time,  weights,  measures,  and  moneys  of  different  countries. 

05 O.  The  scale  of  integers  and  decimals  is  uniform  ;  that  of 
most  denominate  numbers  is  varying. 

The  moneys  of  the  United  States,  Canada,  France,  Italy,  Spain,  Germany, 
Norway  and  Sweden,  Denmark,  Brazil,  Japan,  and  of  some  other  countries,  and 
the  metric  system  of  weights  and  measures,  have  a  uniform  decimal  scale. 

DIVISIONS    OF    TIME. 

151.  The  natural  divisions  of  time  are  the  year  and  the  day, 
the  other  divisions  being  artificial.    The  year  is  the  time  in  which 
the  earth  makes  one  revolution  around  the  sun.     The  day  is  the 
time  in  which  the  earth  makes  one  revolution  on  its  axis. 

152.  The  Solar  Day  is  the  interval  between  two  consecutive 
returns  of  the  sun  to  the  meridian.     On  account  of  the  varying 
motion  of  the  earth  around  the  sun,  the  solar  days  are  of  unequal 
length.    For  civil  purposes  in  measuring  time  the  average  of  all 
the  days  in  the  year  is  taken  as  the  unit. 

4 


50 


DENOMINATE     NUMBERS. 


TABLE. 


60  Seconds  (sec.) 
60  Minutes 
24  Hours 
7  Days 

365  Days,  \ 

52  Weeks,  1  day,  or  >•  =  1  Common  Year 
12  Calendar  Months  ) 

366  Days 
100  Years 


1  Minute min. 

1  Hour hr. 

1  Day da. 

1  Week  .  wk. 


yr. 


1  Leap  Year yr. 

1  Century C. 


NOTE. — In  many  business  transactions  the  year  is  regarded  as  360  days, 
or  12  months  of  30  days  each. 


153.  The  Calendar  Months  with  the  number  of  days  they 
contain  are  as  follows  : 


Season.  Days. 

C  1.  January  (Jan.)  31. 

WINTER.  <  2.  February  (Feb.)  28. 

"  in  leap  year  29. 

(  3.  March  (Mar.)  31. 

SPRING.    <  4.  April  (Apr.)  30. 

(  5.  May  31. 


Season.  Days. 

C  6.  June  30. 

SUMMER.  <  7.  July  31. 

'    8.  August  (Aug.)       31. 

C  9.  September  (Sep.)  30. 
AUTUMN.  <  10.  October  (Oct.)  31. 

'  11.  November  (Nov.)  30. 
WINTER.  12.  December  (Dec.)  31. 


154.  The  Solar  Year  is  the  time  between  two  consecutive 
returns  of  the  sun  to  the  vernal  equinox.  Its  exact  length  is 
365  da.  5  hr.  48  min.  50  sec.  in  mean  solar  time.  For  civil  pur- 
poses, the  year  consists  of  365  or  366  days. 

In  the  calendar  established  by  Julius  Caesar,  B.C.  46,  and  thence  called  the 
Julian  calendar,  three  successive  years  were  made  to  consist  of  305  days  each  ; 
and  the  fourth,  of  366  days.  According  to  the  Julian  calendar,  the  average 
length  of  the  year  was  365^  days,  thus  making  an  error  of  11  min.  10  sec.  each 
year  ;  which  in  400  years  would  amount  to  73  hours,  or  about  3  days.  In  the 
sixteenth  century,  in  consequence  of  the  excess  of  the  Julian  year  above  the 
true  solar  year,  the  error  in  the  calendar  was  10  days.  To  correct  the  calen- 
dar, and  to  prevent  any  error  in  the  future,  Pope  Gregory  XIII.  decreed  that 
10  days  should  be  omitted  in  the  month  of  October,  1582,  and  that  all  centen- 
nial years  not  divisible  by  400  should  be  common  years.  Thus,  the  years 
1700,  1800,  and  1900,  which  according  to  the  Julian  calendar  would  be  leap 
years,  would  according  to  the  reformed  calendar  be  common  years.  This 


LINEAR     MEASURE.       ,  51 

calendar  is  sometimes  called  the  Gregorian  calendar.     It  is  now  used  in  all 
civilized  countries  except  Russia. 

The  Julian  and  Gregorian  calendars  are  also  designated  by  the  terms  Old 
Style  and  New  Style.  In  consequence  of  the  years  1700  and  1800  being  com- 
mon years  by  the  Gregorian  calendar,  the  difference  between  the  two  styles  is 
now  12  days.  Thus,  when  it  is  July  4  in  Russia,  it  is  July  16  in  other  countries. 

155.  KULE  FOR  LEAP  YEARS. —  All  years  divisible,  by  4> 
except  centennial  years,  are  leap  years. 

All  centennial  years  divisible  by  J±00  are  leap  years. 


LINEAR    MEASURE. 

156.  Linear  or  Long  Measure  is  used  in  measuring  dis- 
tances, also  the  length,  breadth,  and  height  of  bodies,  or  their 
linear  dimensions. 

In  measuring  length,  the  yard  derived  from  the  standard  yard  of  England 
is  the  standard  unit,  the  yards  of  the  United  States  and  England  being  iden- 
tical. Theoretically,  the  yard  is  equal  to  f ff§f§  of  the  length  of  a  pendulum 
that  vibrates  seconds  in  a  vacuum,  at  the  level  of  the  sea  in  the  latitude  of 
London  ;  that  is,  a  pendulum  that  vibrates  seconds  under  the  above  conditions 
is  39.1393  inches  in  length.  The  standard  yard  is,  in  fact,  the  distance  be- 
tween two  points  on  a  brass  bar,  preserved  at  Washington,  the  distance  to  be 
taken  when  the  bar  is  at  a  temperature  of  62°  Fahrenheit.  This  bar  was 
obtained  from  England  in  1827. 


TABLE. 


12  Inches  (in.)  =  1  Foot  .     .   ft. 

3  Feet  =  1  Yard  .     .  yd. 

5|  Yards  =1  Rod   .     .  rd. 

40  Rods  =  1  Furlong  fur. 

8  Furlongs      =  1  Mile  .     .  mi. 


mi.   fur.      rd.          yd.          ft.  in. 

1  =  8  =  320  =  1760  =  5280  =  63360 

1  =    40  =    220  =    660  =    7920 

1  =       5£=      16i=      198 

I-       3  =       36 

1  =       12 


NOTES. — 1.  The  inch  is  usually  divided  into  halves,  quarters,  eighths,  and 
sixteenths. 

2.  The  foot  and  inch  are  divided  by  civil  engineers  and  others  into  tenths, 
hundredths,  thousandths,  etc. 

3.  In  measuring  cloth,  ribbon,  and  other  goods  sold  by  the  yard,  the  yard 
is  divided  into  halves,  quarters,  eighths,  and  sixteenths. 

4.  At  the  U.  S.  Custom  Houses  the  yard  is  divided  into  tenths  and  hun- 
dredths. 

5.  The  mile  (5280  ft.)  of  the  above  table  is  the  legal  mile  of  the  United 
States  and  England,  and  hence  it  is  sometimes  called  the  statute  mile. 


52  DENOMINATE    NUMBERS. 

157.   Other    Denominations. — The  following  denomina- 
tions are  also  used  : 


pendulam  makers. 


Point  =  A  Inch. 

1  Line  =  TV  Inch. 

1  Size  =  |  Inch.     Used  by  shoemakers. 

1  Hand  =  4  Inches.     Used  in  measuring  the  height  of  horses. 

1  Fathom  =  6  Feet.     Used  in  measuring  depths  at  sea. 

1  Cable-length        =  120  Fathoms,  or  240  yards. 
1  Geographic  Mile  =  1.15+  Statute  Miles.     Used  in  measuring  distances  at 

sea. 

1  Knot  =  1  Geo.  Mile.     Used  in  determining  the  speed  of  vessels. 

60  Geo.  Miles,  or  )    _  ^  -^  \  of  latitude  on  a  meridian,,  or  of  longitude 

69.16  Stat.  Miles  \  *  }  on  the  equator. 

360  Degrees  =  the  Circumference  of  the  Earth. 


SURVEYORS'     LINEAR    MEASURE. 

158.  Surveyors'  Linear  Measure  is  used  in  measuring 
land,  roads,  etc. 

The  unit  of  this  measure  is  a  chain,  4  rods  or  66  feet  in  length,  called 
Gunter's  Chain.  It  is  divided  into  100  parts  called  links,  each  link  being  7.92 
inches  in  length. 


lOOLinks(^)  =  1  Chain 
80  Chains       —  1  Mile  . 


TABLE. 


ch. 
mi. 


ni.       ch.         ft.  I.  in. 

1  =  80  =  5280  =  8000  =  63360 
1  =      66  =    100  =      792 
.66  =        1  =     7.92 


NOTES. — 1.  Links  are  written  decimally  as  hundredths  of  a  chain. 

2.  1  rod  =  25  links. 

3.  Engineers  for  railroad  and  other  purposes  use  a  chain  or  tape  100  feet 
long,  the  feet  being  divided  into  tenths. 


SQUARE    MEASURE. 
159.  Square  Measure  is  used  in  measuring  surfaces. 

The  unit  of  square  measure  is  a  square  bounded  by  lines  of  some  known 
length.  Thus,  a  square  inch  is  a  square  whose  sides  are  one  inch  long ;  a 
square  foot,  a  square  whose  sides  are  one  foot  long ;  etc. 


SURVEYORS'    SQUARE   MEASURE.  53 

TABLE. 

144   Square  Inches  (sq.  in.)  =  1  Square  Foot  .     .     .     sq.  ft. 

9    Square  Feet  =  1  Square  Yard  .    .     .    sq.  yd. 

30|-  Square  Yards  =  1  Square  Rod  .     .    .    sq.  rd. 

160    Square  Rods  =  1  Acre     ......      A. 

NOTE. — 1  Rood  =  40  sq.  rds.  —  %  A.    The  rood  has  practically  gone  out 
of  use. 

16O.  The  Area  of  a  surface  is  an  expression  for  that  surface 
in  terms  of  square  units. 


4  feet. 


In  the  diagram  each  small  square 
represents  a  square  foot.  Since  there  are 
3  rows,  and  4  square  feet  in  each  row, 
there  are  3  times  4  square  feet,  or  12 
square  feet  in  the  rectangle.  Hence,  the 
area  of  any  rectangle  may  be  found  by 
multiplying  together  the  numbers  denot- 
ing its  length  and  breadth,  in  the  same 
denomination ;  or,  more  briefly, 


To  find  the  area  of  a  rectangle,  multiply  its  length  by 
its  breadth. 


SURVEYORS'     SQUARE     MEASURE. 

161.  Surveyors'  Square  Measure  is  used  in  measuring 
land. 

TABLE. 

10000  Square  Links  (sq.  1)  =  1  Square  Chain  .     .    .   sq.  cli. 
10  Square  Chains  =  1  Acre   .......     A. 

640  Acres  =  1  Square  Mile     .     .     .  sq.  mi. 


NOTES.  —  1.  1  Pole  or  Perch  =  1  sq.  rd.  =  TV  sq.  ch.  = 

2.  The  acre  is  the  common  unit  of  land  measure. 

3.  In  the  vicinity  of  St.  Louis,  and  in  ether  parts  of  the  Mississippi  valley 
that  were  settled  by  the  French,  the  old  French  arpent  is  still  used  as  the 
unit  of  land  measure.     It  contains  about  £  of  an  English  acre. 

162.  U.  S.  Public  Lands  are  divided  by  north  and  south 
lines  run  according  to  the  true  meridian,  and  by  others  crossing 


54 


DENOMINATE     NUMBERS. 


them  at  right  angles,    so  as  to  form   townships   of   six  miles 
square. 

Townships  are  subdivided  into  sections,  containing,  as 
nearly  as  may  be,  640  acres  each,  or  1  square  mile. 

Sections  are  subdivided  into  half -sections,  quarter-sections, 
half -quarter-sections,  and  quarter-quarter-sections. 


1  Township 

1  Section 

1  Half-Section 

1  Quarter-Section 

1  Half-Quarter-Section 

1  Quarter-Quarter-Section  = 


TABLE. 

=  6 mi.  x  6  mi.=  36  sq.  mi.=  23040  A. 

=  1  "    x  1  "  =   1  "  =  640  " 

=  1  "    x  i  "  =  i  "  ==  320  " 

=  i  <tf    x  i  "  =  i  "  =  160  " 

x  i  "  =  t  "  =  80  " 

:    X  1  "  =  JL  "  =  40  " 


The  following  diagrams  show  the  method  of  numbering  the  sections  of  a 
township,  as  also  that  of  naming  the  subdivisions  of  sections. 


A  TOWNSHIP. 
H 


W 


6 

5 

4 

3 

2 

1 

7 

8 

9 

10 

11 

12 

18 

17 

16 

15 

14 

13 

19 

20 

21 

22 

23 

24 

30 

29 

28 

27 

26 

25 

31 

32 

33 

34 

35 

36 

E     W 


A  SECTION. 

N 

N.i 

320  A. 

N.W.  1 

of 

s.w.  \ 

40  A. 

E  i 
of 

S.  E.  £ 

S.W.  i 
of 

S.W.   5 

80  A 

160  A 

S.W.  { 

40  A. 

SOLID    OR    CUBIC     MEASURE. 

163.  Solid  or  Cubic  Measure  is  used  in  measuring  solids, 
or  bodies,  which  have  length,  breadth,  and  thickness  or  depth ; 
as  boxes,  earth,  wood,  stone,  etc. 

The  unit  of  cubic  measure  is  a  cube,  each  of  whose  edges  is  a  unit  of  some 
known  length.  Thus,  a  cubic  inch  is  a  cube,  each  of  whose  edges  is  one 
inch  ;  a  cubic  foot  is  a  cube,  each  of  whose  edges  is  one  foot ;  etc. 


SOLID     OR      CUBIC    MEASURE. 


55 


4  Feet 


\\ 


TABLE. 

1728  Cubic  Inches  (cu.  in.)  =  1  Cubic  Foot  ....  cu.ft. 
27  Cubic  Feet  =  1  Cubic  Yard  .     .    .    .  cu.ycl 

NOTES. — 1.  128  cubic  feet  =  1  cord  of  wood,  or  bark.     Tanners,  in*  meas- 
uring bark,  use  a  measure  in  which  the  foot  is  divided  into  tenths. 

2.  The  U.  S.  measurement  ton  for  freight  contains  40  cubic  feet. 

3.  The  IT.  S.  register  tonnage  (entire  internal  cubical  capacity)  of  vessels 
is  expressed  in  tons  of  100  cubic  feet  each. 

164.  The  Volume   or   Solid  Contents   of  a  solid  is  an 
expression  for  that  solid  in  terms  of  cubic  or  solid  units. 

The  diagram  represents  a  solid  4  feet  long,  3  feet  broad,  and  2  feet  thick. 
Each  small  cube  is  a  cubic  foot. 
Since  the  end  of  the  solid  contains 
(3  x  2)  6  square  feet  of  surface,  it 
is  evident,  if  a  section  1  foot  thick 
be  cut  off  from  this  end,  it  can  be 
divided  into  6  cubes,  with  edges  1 
foot  in  length,  and  therefore  the 
section  will  contain  6  cubic  feet  ; 
and  since  the  whole  solid  is  4  feet 
long,  and  contains  4  like  sections, 
it  must  contain  4  times  6  cubic 
feet,  or  twenty-four  cubic  feet. 
Hence  the  volume  of  a  rectangular 
solid  may  be  found  by  multiplying 
together  the  numbers  expressing 
its  length,  breadth,  and  thickness,  in  the  same  denomination ;  or,  more 
briefly, 

To  find  the  volume  of  a  rectangular  solid,  multiply 
together  its  length,  breadth,  and  thickness. 

165.  Lumber  is  measured  by  board  measure.     The  board 
foot  is  1  ft.  long,  1  ft.  wide,  and  1  in.  thick  ;  hence  it  is  T^  of  a 
cubic  foot. 

Boards,  plank,  scantling,  joists,  and  sawed  timber  generally  are  usually 
measured  by  board  measure ;  hewn  and  round  timber  by  cubic  measure. 

166.  When  lumber  is  not  more  than  one  inch  thick,  to  find 
the  number  of  feet  board  measure  :  Multiply  the  length  in  feet  by 
the  width  in  inches,  and  divide  the  product  by  12. 

When  more  than  1  inch  thick  :  Multiply  the  length  in  feet  by 
the  width  and  thickness  in  inches,  and  divide  the  product  by  12. 


56  DENOMINATE    NUMBERS. 


LIQUID    MEASURE. 
167.  Liquid  Measure  is  used  for  measuring  liquids. 

The  unit  of  this  measure  is  the  wine  gallon,  which  contains  231  cubic 
inches. 

TABLE. 

gal         qt.       pt. 

4  Gills  (gi.)  —  1  Pint    .    .    .    pt.  1   =  4  =  8  =  32 

2  Pints          =  1  Quart  .     .     .     qt. 
4  Quarts       =  1  Gallon     .     .  gal. 

NOTES. — 1.  In  estimating  the  capacity  of  tanks,  cisterns,  reservoirs,  etc., 
1  barrel  =  31^  gallons ;  1  hogshead  =  2  barrels  =  63  gallons. 

2.  In  commerce,  the  barrel  and  hogshead  are  not  fixed  measures,  but  their 
capacity  is  found  by  gauging,  or  actual  measurement. 

3.  The  imperial  gallon  of  England  contains  277.274  cubic  inches,  and  is 
equivalent  to  1.2  U.  S.  wine  gallons. 

4.  The  beer  gallon  contains  282  cubic  inches.     It  is  no  longer  used  in  the 
United  States. 


APOTHECARIES'     FLUID     MEASURE. 

168.  Apothecaries'  Fluid  Measure  is  used  in  prescrib- 
ing and  compounding  liquid  medicines. 

The  gallon  and  pint  of  this  measure  are  the  wine  gallon  and  pint. 

TABLE. 

Cong.  0.    /§.     fi.       ni. 


60  Minims  (til)    =  1  Fluidrachm     .    /3  . 

8  Fluidrachms  =  1  Fluidounce      .    /§  . 
16  Fluidounces  =  1  Pint  ....        0. 

8  Pints  =  1  Gallon  .     .     .  Cong. 


1  =  8  =  128  =  1024  =  61440 
1  =  16  =  128  =  7680 
1  =   8  =   480 
1  =   60 

\ 

NOTES. — 1.  Cong,  is  for  the  Latin  congius,  gallon  ;  0.,  for  the  Latin  octa- 
rius,  one-eighth. 

2.  The  symbols  precede  the  numbers  to  which  they  refer ;  thus,  0.  6 
/§  10,  is  6  pints  10  fluidounces. 


DRY    MEASURE. 

169.  Dry  Measure  is  used  in  measuring  dry  articles ;  as 
salt,  grain,  fruits,  etc. 


APOTHECARIES       WEIGHT. 


57 


llie  jinit  of  this  measure  is  the  Winchester  bushel,  which  contains  2150.43 
cubic  inches. 


2  Pints  (pt.)  =  I  Quart 
8  Quarts         =  1  Peck 
4  Pecks          =  1  Bushel 


TABLE. 

.     .     gt. 

.  pk. 
bu. 


bu.       pk.         qt.         pt. 

I  =  4  =  32  =  64 

1  =     8  =  16 

1=2 


NOTES. — 1.  The  half-peck  or  gallon  of  this  measure  contains  268.8  cubic 
\inches. 

2.  The  imperial  bushel  of  England  contains  2218.19  cubic  inches,  and  is 
equal  to  1.03  Winchester  bushels. 

3.  Grain,  seeds,  etc.,  are  usually  sold  by  weight.     For  table  of  equivalents 
see  Art.  173. 


TROY    "WEIGHT. 

17O.  Troy  Weight  is  used  in  weighing  gold,  silver,  coins, 
and  jewels  ;  also  in  philosophical  experiments. 

The  unit  of  weight  is  the  Troy  pound,  which  contains  5760  grains.  A 
cubic  inch  of  distilled  water  weighs  252.458  of  these  grains,  when  the  height 
of  the  barometer  is  30  inches,  and  the  temperature  of  the  air  and  water  62° 
Fahrenheit. 


TABLE. 

24  Grains  (gr.)  =  1  Pennyweight  pwt. 
20  Pennyweights  =  1  Ounce  .  .  .  oz. 
12  Ounces  =  1  Pound  .  Ib. 


lb.      oz.       pwt.         gr. 
1  =  12  =  240  =  5760 
1  =    20  =    480 
1=      24 


NOTE. — The  carat,  used  in  weighing  diamonds,  equals  3.2  Troy  grains. 
The  term  carat  is  also  used  to  denote  the  fineness  of  gold,  and  means  ^ 
part.     Thus,  gold  18  carats  fine  contains  18  parts  pure  gold  and  6  parts  alloy. 


APOTHECARIES'     WEIGHT. 

171.   Apothecaries'   "Weight  is  used  in  prescribing  and 
compounding  medicines  not  liquid. 

The  pound,  ounce,  and  grain  of  this  weight  are  the  same  as  those  of  Troy 
weight,  the  division  of  the  ounce  being  different, 


OF  THE 

UNIVERSITY 


58  DENOMINATE   NUMBERS. 

TABLE. 


20  Grains  (gr.)  =  1  Scruple  .  .  sc.  or  3. 

3  Scruples       =  1  Dram  .  .  dr.  or  3  . 

8  Drams          —  1  Ounce  .  .  oz.  or  § . 

12  Ounces         =  1  Pound  .  Ib.  or  ft . 


ft       §        3         3         gr. 

1  =  12  =  96  =  288  =  5760 

1  =    8  =    24  =    480 

1  =      3  =      60 

1  =      20 


NOTES.— 1.  The  symbols  precede  the  numbers  to  which  they  refer ;  thus, 
6  3  4,  is  6  ounces  4  drams. 
2.  Drugs  and  medicines  are  sold  in  large  quantities  by  Avoirdupois  weight. 


AVOIRDUPOIS    "WEIGHT. 

Avoirdupois  "Weight  is  used  in  weighing  all  articles, 
excepting  gold,  silver,  precious  stones,  and  medicines  in  small 
quantities. 

The  Avoirdupois  pound  contains  7000  Troy  grains. 


TABLE. 

16  Ounces  (oz.)          =     1  Pound      .     .     .     .  Ib. 
100  Pounds                 =  \  l  Hu°<^-weight,  or  cwt. 
(  I  Cental      ....    (7. 
Hundred-weight  =     1  Ton T. 


T.     cwt.       Id.  oz. 

\  =  20  =  2000  =  32000 
1  =    100  =    1600 
1=       16 

NOTES. — 1.  The  ounce  is  divided  into  halves  and  quarters. 

2.  The  dram,  TV  of  an  ounce,  is  now  little  used,  except  by  silk  manufacturers. 

3.  The   Long  or  Gross  ton,  formerly  used,  contained  2240  pounds ;  the 
hundred-weight,  112  pounds  ;  and  the  quarter,  28  pounds. 

J  These  weights  are  still  used  at  the  U.  S.  Custom  Houses,  in  ocean  freights, 
ind  in  freighting  and  wholesaling  coal  from  the  mines. 

173.  In  buying  and  selling  grain,  seeds,  and  other  produce, 
the  bushel  is  regarded  as  a  certain  number  of  pounds.  The 
Boards  of  Trade  of  several  of  our  leading  cities,  and  the  people 
generally,  use  the  equivalents  given  in  the  following  table  :  * 

*  These  weights  are  the  same  as  prescribed  by  the  laws  of  most  States,  but  the  laws  are 
not  uniform.  In  inter-state  commerce  it  is  necessary  to  have  common  units,  although  they 
may  differ  from  the  units  established  by  law.  The  laws  are  generally  disregarded  where  the 
units  prescribed  by  them  differ  from  those  prescribed  by  custom,  or  the  laws  of  most  of  the 
States.  As  an  instance  of  this  irregularity,  the  State  of  New  York  prescribes  58  pounds  as  a 
bushel  of  corn,  but  the  Boards  of  Trade  and  custom  generally  adopt  56  pounds  as  a  bushel 
of  corn.  There  can  be  no  doubt  but  that  an  appeal  to  the  courts  of  any  one  of  the  States 
would  lead  to  a  decision  in  accordance  with  the  laws  of  that  State  in  fixing  the  weight  of  a 
bushel  of  grain.  It  is  further  evident  that  decisions  in  State  courts  of  last  appeal  might  be 
as  discordant  upon  this  subject  as  the  laws  themselves. 


CIRCULAR    MEASURE.  59 

TABLE  OF  AVOIRDUPOIS  POUNDS  IN  A  BUSHEL. 


Commodities. 

Lbs. 

Commodities. 

Lbs. 

Commodities. 

Lbs. 

\ 

Barley         .  •    •  . 

48 

•^Corn   shelled.  .  . 

56 

,  Peas  

60 

i 

Beans 

60 

Corn  in  the  ear. 

70 

*Rye 

56 

Buckwheat 

48 

\Malt     

34 

y  Timothy  Seed 

45 

PloVPT    SpP(l 

60 

^Oats     

32 

•Wheat 

60 

In  the  Liverpool,  San  Francisco,  and  some  other  markets,  produce  is 
bought  and  sold  by  the  cental  of  100  pounds.  Railway  freight  tariffs  in  the 
United  States  on  grain,  provisions,  etc.,  are  reckoned  per  cwt.  or  cental, 

V  174.  The  following  units  are  used  in  commerce  : 

1  Quintal  of  Fish  =  100  Ibs. 

1  Barrel  of  Flour  —  196  Ibs* 

1  Barrel  of  Pork  =  200  Ibs. 

3— Gallon  Refined  Petroleum  =  6J  Ibs. 

1  Gallon  Crude  Petroleum  =  6-J-  Ibs. 

I  Keg  of  Nails  =  100  Ibs. 


CIRCULAR     MEASURE. 

V  175.  Circular  or  Angular  Measure  is  used  in  measuring 
angles  and  arcs  of  circles.  It  is  employed  principally  by  surveyors 
in  determining  directions,  by  navigators  in  determining  latitude 
and  longitude  of  places,  and  by  astronomers  in  making  observa- 
tions. 

The  unit  of  this  measure  is  the  degree,  which  is  ^^  of  the  circumference 
of  any  circle. 


GO  Seconds  (  ' 

TABLE. 
')  —  1  Minute     .     . 

f 

60  Minutes 

:  1  Desree 

o 

360  Degrees 

—  1  Circle  . 

.    .    .    C 

In  order  to  prevent  confusion,  to  remove  the  discrepancies  which  now  exist,  and  to  facil- 
itate commerce,  it  is  to  be  hoped  that  Congress  will  enact  general  laws  on  the  subject, 
making  the  equivalents  of  a  bushel  uniform,  or  introducing  the  cental  (or  still  better  the 
metric)  system. 

*  It  is  recommended  by  the  leading  Boards  of  Trade  that  all  barrel  flour  contain  200 
pounds,  and  all  sack  flour  50,  100,  150,  or  200  pounds. 

Flour  is  frequently  exported  from  the  United  States  to  Great  Britain  in  sacks  of  140 
pounds  each.  The  sack  of  Great  Britain  usually  contains  280  pounds. 


00  UNITED     STATES     MONET. 


!.  A  quadrant  is  one-fourth  of  a  circle,  or  90°. 

2.  A  sextant  is  one-sixth  of  a  circle,  or  60°. 

3.  1  minute  of  the  circumference  of  the  earth  is  called  a  nautical,  or 
geographic  mile,  and  is  about  1.15  statute  or  common  miles. 


COUNTING. 
176.  The  following  table  is  used  in  counting  certain  articles  : 


12  Units  =  1  Dozen  .  .  .  doz. 
12  Dozen  =  1  Gross  ....  gr. 
12  Gross  =  1  Great  Gross  .  g.  gr. 


g.  gr.    gr.         doz.        units. 

1  =  12  =  144  =  1728 

1  =     12  =    144 

1  =:       12 


PAPER. 

177.  The  following  table  is  used  in  the  paper  trade  : 

i 
24  Sheets       =  1  Quire    .    .    .    qr. 


20  Quires      =  1  Ream     .    .    .   rm. 


rm.       qr.        sheets. 
1  =  20  =  480 


2  Eeams      =  1  Bundle.  1  =     24 

5  Bundles   =  1  Bale. 


UNITED    STATES     MONEY. 

178.  United  States  Money  is  the  legal  currency  of  the 
United  States.     It  consists  of  gold  coins,  silver  coins,  treasury 
notes,  and  national  bank  notes. 

179.  Legal  Tender. — The  term  legal  tender  is  applied  to 
money  which  may  be  legally  offered  in  the  payment  of  debts. 

180.  The  unit  of  value  is  the  gold  dollar  of  25.8  grains. 

TABLE. 

10  Mills  =  1  Cent c.,ct. 

10  Cents  =  1  Dime      ....      d. 

10  Dimes  or  100  Cents  =  1  Dollar     ....      $. 

10  Dollars  =  1  Eagle      ....      E. 

NOTES. — 1.  In  business  operations,  dollars  and  cents  are  principally  used. 
Eagles  and  dimes  are  used  only  as  the  names  of  coins. 


DENOMINATE     NUMBERS. 


61 


2.  In  writing  U.  S.  money,  the  decimal  notation  is  used.     Dollars  are 
written  at  the  left  of  the  separatrix  and  form  the  integral  part.     Cents  are 
written  as  hundredths  of  a  dollar,  and  occupy  the   first  two  places  at  the 
right  of  the   separatrix.     Mills  are  written  as  thousandths  of  a  dollar,  and 
occupy  the  third  decimal  place. 

Usually,  in  the  final  results  of  business  operations,  if  the  mills  are  more 
than  five,  they  are  regarded  as  an  additional  cent ;  if  less  than  five,  they  are 
rejected. 

3.  In  checks,  notes,  drafts^  etc.,  cents  are  usually  written  as  hundredths  of 
a  dollar  in  the  form  of  a  fraction.     Thus,  six  dollars  and  twenty-five  cents  may 
be  written,  $6T%5ff. 

181.  The  legal  coins  of  the  United  States  are  as  follows  : 

SILVER. 

Weight. 
412|  grains. 


Weight 
in  grains. 

1  dollar  piece,             25.8 

2|  dollar  piece,  or 
Quarter-eagle, 

.   64.5 

3  dollar  piece, 

77.4 

5  dollar  piece,  or 
Half-eagle, 

129. 

10  dollar  piece,  or 
Eagle, 

•258. 

20  dollar  piece,  or 
Double-eagle, 

>516. 

12|  grams,  or  192.9  grains. 
6J  grams,  or  96.45  grains. 


Standard  dollar, 
Half  dollar,  or  ) 

50  cent  piece,  ( 
Quarter  Dollar,  or 

25  cent  piece, 
Dime,  or 

10  cent  piece, 

COPPER  AND  NICKEL. 

5  cent  piece,  5  grams,  or  77.16  grains. 

3  cent  piece,  30  grains. 

1  cent  piece,  48  grains. 


The  Mill  is  not  coined. 


^  183.  The  Trade  Dollar  contains  420  grains  of  standard 
silver  (.900  fine).  It  is  not  now  coined,  and  is  not  a  legal  lender. 
It  was  originally  coined  for  the  purposes  of  trade  in  China  and 
Japan. 

^  183.  The  gold  and  silver  coins  of  the  United  States  contain  9 
parts  by  weight  of  pure  metal  and  1  part  alloy.  The  alloy  of 
silver  coins  is  copper;  and  the  alloy  of  gold  coins,  copper,  or 
copper  and  silver.  (The  silver  in  no  case  exceeds  -fa  of  the  whole 
alloy.) 

184.  Gold  Coins  are  a  "legal  tender  in  all  payments  at 
their  nominal  value  when  not  below  the  standard  weight  and 
limit  of  tolerance"*  provided  bylaw;  and,  "when  reduced  in 


*  "  Any  gold  coin  of  the  United  States,  if  reduced  in  weight  by  natural  abrasion  not 
more  than  one-half  of  one  per  centum  below  the  standard  weight  prescribed  by  law,  after  a 


C2  DENOMINATE     NUMBERS. 

weight,  below  said  standard  and  tolerance,  are  a  legal  tender  at 
\  valuation  in  proportion  to  their  actual  weight." 

^  185.  Standard  Silver  Dollars  are  "  a  legal  tender  at  their 
nominal  value  for  all  debts  and  dues,  public  and  private,  except 
where  otherwise  expressly  stipulated  in  the  contract."  "The 
Secretary  of  the  Treasury  is  authorized  and  directed  to  purchase 
*  *  *  silver  bullion  *  *  *  not  less  than  $2,000,000  worth 
per  month,  nor  more  than  $4,000,000  worth  per  month,  and 
cause  the  same  to  be  coined  monthly,  as  fast  as  so  purchased,  into 
\  such  dollars."  (Act  of  Feb.  28,  1878,  Sec.  1.) 

^  186.  Silver  Certificates.— Any  holder  of  standard  silver 
dollars  ' '  may  deposit  the  same  with  the  Treasurer,  or  any  Assist- 
ant Treasurer  of  the  United  States,  in  sums  not  less  than  $10, 
and  receive  therefor  certificates  of  not  less  than  $10,  each  corres- 
ponding with  the  denominations  of  United  States  notes  "  (189). 
These  certificates  are  "receivable  for  customs,  taxes,  and  all 
public  dues,  and  when  so  received  may  be  reissued."  (Act  of  Feb. 
28,  1878,  Sec.  4.) 

187.  Subsidiary  Coins.— "The  present  (1880)  silver  coins 
of  the  United  States  of  smaller  denominations  than  $1"  are  "a 
legal  tender  in  all  sums  not  exceeding  $10,  in  full  payment  of  all 
dues,  public  and  private."     (Acts  of  1st  session,  46th  Congress, 
Chap.  XII,  Sec.  3.) 

"  The  holder  of  any  of  the  silver  coins  of  the  United  States  of  smaller 
denominations  than  $1  may,  on  presentation  of  the  same  in  sums  of  $20,  or 
any  multiple  thereof,  at  the  office  of  the  Treasurer  or  any  Assistant  Treasurer 
of  the  United  States,  receive  therefor  lawful  money  of  the  United  States." 
(Acts  of  1st  session,  46th  Congress,  Chap.  XII,  Sec.  1.) 

188.  Minor  Coins. — The   5   and  3   cent  pieces  contain  J 
copper  and  J  nickel.     The  1  cent  piece  contains  95  per  cent, 
copper  and  5  per  cent,  tin  and  zinc.     These  coins  are  "  a  legal 
tender,  at  their  nominal  value,  for  any  amount  not  exceeding 
twenty-five  cents  in  any  one  payment." 

189.  United   States  Notes  ("Greenbacks")  are  "a  legal 
tender  for  all  debts,  public  and  private,  except  duties  on  imports 

circulation  of  twenty  years,  as  shown  by  its  date  of  coinage,  and  at  a  ratable  proportion  for 
any  period  less  than  twenty  years,  is  received  at  its  nominal  value  by  the  United  States 
treasury  and  its  offices."  The  "Coinage  Act  of  1873"  allows  a  deviation  from  the  standard 
weight  of  I  of  a  grain,  or  less,  in  the  manufacture  of  the  dollar  piece. 


ENGLISH    MONEY.  63 

and  interest  on  the  public  debt."  Since  Jan.  1,  1879,  they  have 
been  redeemable  "  in  coin  *  *  *  on  their  presentation  for 
redemption  at  the  office  of  the  Assistant  Treasurer  of  the  United 
States  in  the  City  of  New  York,  in  sums  of  not  less  than  $50." 
They  represent  the  values  of  $1,  $2,  $5,  $10,  $20,  $50,  $100,  $500, 
$1000,  $5000,  and  $10,000.  The  Act  of  May  31,  1878,  fixed  their 
value  at  $346,681,016,  and  forbade  their  further  contraction. 

190.  National  Bank  Notes  are  not  a  legal  tender  ;  but, 
since  they  are  "  secured  by  bonds  of  the  United  States  deposited 
with  the  U.  S.  Treasurer  at  Washington,"  and  are  redeemed  in 
lawful  money  by  the  national  banks  and  the  Treasurer  of  the 
United  States,  they  are  usually  accepted  in  the  payment  of  debts 
in  any  part  of  the  United  States.     They  are  "receivable  in  all 
parts  of  the  United  States  in  payment  of  all  taxes  and  excises  and 
all  other  dues  to  the  United  States  except  duties  on  imports,  and 
also  for  salaries  and  other  debts  and  demands  owing  by  the  United 
States  to  individuals,  corporations,  and  associations  within  the 
United  States  except  interest  on  the  public  debt." 

They  represent  the  values  of  $1,  $2,  $5,  $10,  $20,  $50,  $100, 
$500,  and  $1000.  Since  Jan.  1,  1879,  no  notes  of  the  denomina- 
tion of  $1  and  $2  have  been  issued  to  national  banks  (R.  S.  5175). 
Since  the  act  of  Jan.  14,  1875,  the  volume  of  national  bank  notes 
has  been  unlimited.  Nov.  1,  1879,  their  total  circulation,  includ- 
ing gold  banks,  was  $337,181,418. 

ENGLISH     MONEY. 

191.  English  or  Sterling  Money  is  the  legal  currency  of 
Great  Britain. 

TABLE.  Value  in 

TJ.  S.  money. 

4  Farthings  —     1  Penny     .     .     .     d.     .     .     .     $  .02  + 
12  Pence          =     1  Shilling  .     .'•'-.*  .....  243  + 


20  Shillings    =  >         •    •  .     .    .      4.8665 

(1  Sovereign  > 

*"  NOTES.—  1.  1  Crown  =  5  shillings,  or  }  of  a  pound  ($1.216  +  ). 
•^   2.  1  Guinea  =  21  shillings  ($5.11).     It  is  not  now  coined. 

3.  The  gold  coins  of  Great  Britain  are  22  carats  (|i),  or  .916|  fine.     (The 
old  carat  system  (170,  note)  is  generally  abandoned  except  for  jewelry.     1 
carat  =  .041f.) 

4.  The  silver  coins  of  Great  Britain  are  .925  (f£)  fine. 


DENOMINATE    NUMBERS. 


192.   FOKEIGN  MONEYS  or  ACCOUNT  AND  THEIR  VALUES  IN- 
UNITED  STATES  MONEY. 


Country. 

Monetary  Unit. 

Standard. 

Value  in 
U.  S.  Money. 

Florin  of  100  kreutzers  . 

Silver. 

.40  7 

•Franc  of  100  centimes  . 

Gold  and  silver 

.19  3 

Bolivia  

bBoliviano,  100  centavos 

Silver 

.82  3 

Brazil  

Milreisof  1000  reis  

Gold    .    . 

.54  6 

British  America.  .  . 

Dollar  of  100  cents  

Gold  

$1.00 

Chili    .  .  . 

Peso  of  100  centavos  .  . 

Gold  and  silver 

91  2 

Cuba  

Peso  of  100  centavos.  .  . 

Gold  and  silver 

.93  2 

c  Crown  of  100  ore  

Gold  

.26  8 

Ecuador  

bPeso  of  100  centavos  .  . 

Silver   . 

.82  3 

Egypt.    , 

Piaster  of  40  paras 

Gold    .  .  . 

049 

France 

a  Franc  of  100  centimes 

Gold  and  silver 

19  3 

Great  Britain 

Pound  sterling1. 

Gold 

4  86  64 

Greece  

•Drachma  of  100  lepta  . 

Gold  and  silver.  .. 

.19,3 

German  Empire 

Mark  of  100  pfennige 

Gold 

23  8 

India  „ 

Rupee  of  16  annas  d  . 

Silver  

.89 

Italy  

"Lira  of  100  centesimi 

Gold  and  silver.  . 

.19  3 

Japan  .  .  . 

Yen  of  100  sen  

Silver  

88  8 

Liberia  .  .  . 

Dollar  of  100  cents  .  .  . 

Gold   

1  00 

Mexico 

Dollar  of  100  centavos 

Silver  

89  4 

Netherlands  

Florin  of  100  cents  

Gold  and  silver.  .  . 

.40,2 

Norway  

c  Crown  of  100  ore  

Gold  

.26  8 

Peru 

bSol  of  100  centavos 

Silver 

82  3 

Portugal  

Milreis  of  1000  reis  .  . 

Gold  

1.08 

Russia    

Rouble  of  100  copecks. 

Silver  

.65  8 

Sandwich  Islands 

Dollar  of  100  cents  .  .  . 

Gold  

1.00 

•Peseta  of  100  centimes. 

Gold  and  silver 

19  3 

Sweden  

0  Crown  of  100  ore  

Gold    

26  8 

Switzerland    
Tripoli 

•Franc  of  100  centimes. 
Mahbub  of  20  piasters 

Gold  and  silver... 
Silver 

.19,3 

74  3 

Turkey 

Piaster  of  40  paras 

Gold 

04  4 

U  S.  of  Colombia  . 

bPeso  of  100  centavos  .  . 

Silver  

.82  3 

Venezuela  

•Bolivar  

Gold  and  silver.  . 

.19  3 

The  above  rates,  proclaimed  by  the  Secretary  of  the  Treasury,  Jan.  1, 
1881,  are  used  in  estimating,  for  Custom-House  purposes,  the  values  of  all 
foreign  merchandise  made  out  in  any  of  said  currencies. 

(•)  The  franc  of  France,  Belgium,  and  Switzerland,  the  peseta  of  Spain, 
the  drachma  of  Greece,  the  lira  of  Italy,  and  the  bolivar  of  Venezuela  have 
the  same  value. 

(b)  The  peso  of  Ecuador,  and  United  States  of  Colombia,  the  boliviano  of 
Bolivia,  and  the  sol  of  Peru  have  the  same  value. 

(c)  The  crowns  of  Norway,  Sweden,  and  Denmark  have  the  same  value. 

(d)  The  anna  contains  12  pies. 


REDUCTION.  65 


REDUCTION. 

193*  Reduction  of  Denominate  Numbers  is  the  chang- 
ing their  denomination  without  changing  their  value. 

194.  To  reduce  denominate  numbers  from  higher  to 
lower  denominations. 

Ex.     How  many  pence  in  £8  16s.  Id.  ? 

OPERATION. 

£      s.      d. 

8    16     7 

OQ  ANALYSIS. — Since  there  are  twenty  shillings  in  1  pound, 

in  8  pounds  there  are  8  times  20  shillings,  or  160  shillings. 
160s.  (For  convenience  multiply  by  20  as  an  abstract  number.) 

16s.  160  shillings  plus  16  shillings  equal  176  shillings.     Since 

i  r/c«  there  are  12  pence  in  1  shilling,  in  176  shillings  there  are 

1  „  176  times  12  pence,  or  2112  pence.     2112  pence  plus  7  pence 

equal  2119  pence.    When  possible,  add  mentally  the  num- 
ber of  the  lower  denomination  to  the  product. 


195.  KTJLE. — Multiply  the  number  of  the  highest  denom- 
ination given  by  the  number  of  the  next  lower  denomina- 
tion required  to  make  1  of  this  higher,  and  to  the  product 
add  the  given  number,  if  any,  of  such  lower  denomination. 

Treat  this  result,  and  the  successive  results  obtained.,  in 
lilce  manner  until  the  number  is  reduced  to  the  required 
denomination. 

EXAMPLES. 

196.  Eeduce: 

1.  £9  13s.  lOrf.  to  pence.  11.  5  mi.  36  rd.  lift,  to  feet. 

2.  6  gal.  3  qt.  1  pt.  to  gills.  12.  456  miles  to  feet. 

8.  £112  18s.  5d.  to  farthings.  13.  16-J-  hands  to  inches. 

4.  6  T.  12  cwt.  65  Ib.  to  pounds.  14.  3  mi.  46  ch.  75  I  to  links. 

5.  The  year  1896  to  hours.  15.  7  mi.  55  ch.  to  rods. 

6.  The  year  1881  to  minutes.  16.  29  sq.  rd.  to  square  feet. 

7.  £245  15s.  3  far.  to  farthings.  17.  97  sq.rd.  to  square  yards. 

8.  48  bu.  3  pk.  6  qt.  to  quarts.  18.  5  sq.  mi.  to  acres. 

9.  The  year  1900  to  hours.  19.  5  miles  square  to  acres. 
10.  18  Ib.  8  oz.  to  pennyweights.  W.  16  cords  112  cu.ft.  to  cu.ft. 

5 


66  DENOMINATE     NUMBERS. 

21.  How  many  cubic  feet  in  a  vessel  whose  measurement  is 
2135  tons  ? 

22.  How  many  pounds  in  16  T.  3  qr.  18  lb.  (Long  Ton  Table)  ? 

23.  How  many  quarts  in  3  libl.  24  gal.  cider  ? 

24.  How  many  pounds  in  2375  bushels  corn  ? 

25.  At  1  cent  each,  what  is  the  value  of  20  great  gross  pens  ? 

26.  How  many  days  from  Jan.  1,  1888,  to  Jan.  1,  1906  ? 

27.  How  many  days  in  8  m.  26  da.  ? 

197.  To  reduce  denominate  numbers  from  lower  to 
higher  denominations. 

Ex.    Eeduce  2119  pence  to  higher  denominations. 

OPERATION.  ANALYSIS.  —  Since   there  are  12  pence  in  1 

12  )  2119^7.  shilling,  in  2119  pence  there  are  as  many  shillings 

20  )  176s  4-  Id  as  -^  Pence  are  contained  times  in  2119  pence,  or 

176   shillings,    and    7   pence   remaining.       Since 

there  are  20  shillings  in  1  pound,  in  176  shillings 

2119c£.  —  .£8  16s.  7d.        there  are  as  many  pounds  as  20  shillings  are  con- 
tained times  in  176  shillings,  or  8  pounds,  and  16 
shillings  remaining.     Therefore,  2119tf.  =  £8  16s.  Id. 


198.  RULE.  —  Divide  the  given  number  by  the  number  of 
that  denomination  required  to  make  1  of  the  next  higher, 
reserving  the  remainder,  if  any,  as  part  of  the  answer. 

Treat  the  quotient,  and  the  successive  quotients  obtained, 
in  like  manner  until  the  number  is  reduced  to  the  inquired 
denomination.  The  last  quotient  and  the  several  remain- 
ders will  form  the  answer. 

EXAM  PLES. 

199.  Reduce 

1.  8475^.  to  pounds.  11.  13387^.  to  pounds. 

2.  9683  cu.ft.  to  cords.  12.  10224  ft.  to  fathoms. 

3.  7534  pte.  to  bushels.  18.  60427  J.  to  chains. 
4>  9817  pts.  to  barrels.  14.  16338/tf.  to  chains. 

5.  5280  ft.  to  miles.  *  15.  5384  rods  to  chains. 

6.  7633  sq.yds.  to  sq.  rds.  16.  6375  I  to  rods. 

7.  8437  days  to  com.  yrs.  17.  5316  sq.  rds.  to  acres. 

8.  6375  hrs.  to  weeks.  18.  49380  sq.  I.  to  acres. 

9.  9537  sec.  to  hours.  19.  38425  sq.  ch.  to  sq.  mi. 
10.  6239  in.  to  rods.  20.  7685  poles  to  acres. 


REDUCTION    OF    DENOMINATE     FRACTIONS.      67 

21.  What  is  the  cost  of  465  yards  of  cloth  at  9J  pence  per 
yard? 

22.  What  is  the  value  of  49375  pounds  of  corn  at  $0.64  per 
bushel  ? 

23.  What  is  the  value  of  27425  pounds  of  corn  at  $0.95  per 
cental  ? 

24.  Required  the  value  of  18643  pounds  of  oats  at  75  cts.  per 
bushel. 

25.  Find  the  cost  of  17387  pounds  of  oats  at  $1.88  per  cental. 

26.  The  report  of  a  cannon  is  heard  4|-  seconds  after  the  flash 
is  seen ;  what  is  the  distance  of  the  cannon,  if  sound  moves  1090 
feet  per  second  ? 

27.  What  cost  21370  pounds  of  straw  at  $8  per  ton  ? 

28.  Required  the  cost  of  875  pounds  of  feed  at  $1.15  per  cwt. 

29.  In  327  days,  how  many  months  of  30  days  each  ? 

SO.  What  is  the  freight  of  39445  pounds  of  merchandise  at  64s. 
per  ton  of  2240  pounds  ? 


REDUCTION     OF     DENOMINATE     FRACTIONS. 

200.  A  Denominate  Fraction  is  a  fraction  whose  integral 
unit  is  a  denominate  number. 

The  principles,  analyses,  and  rules  of  denominate  fractions  are  essentially 
the  same  as  those  of  denominate  integers ;  therefore,  no  special  rules  are 
necessary  for  their  reduction. 

A  sufficient  number  of  illustrative  examples  are  given  to  fully  explain  the 
different  cases  that  may  arise. 

201.  To  reduce  denominate  fractions  from  higher  to 
lower  denominations. 

Ex.    Reduce  T\  of  a  £  to  pence. 

ANALYSIS. — Since  there  are  20  shillings 
in  £1,  in  TV  (.4375)  of  a  £  there  are  TV 

i     x  A  —  _3  5  5<  (.4375)  of  20  shillings,  or  -^  (8.75)  shillings. 

V  Since  there  are  12  pence  in  1  shilling,  in  %5 

35_  ><   A  —  1056/.  (8.75)  shillings  there  are  \5-  (8.75)  times  12 

pence,   or   105   pence.     Or,   multiply  the 

5  3  given  fraction  by  the  numbers  of  the  scale 

Or>  A  x  ^  X  ^T  —  105(?.       required  to  reduce  its  denomination  to  the 

required  denomination. 


68 


DENOMINATE    NUMBERS. 


Ex.  Eeduce  .4375  of  a  £  to  pence. 

OPERATIONS. 

.4375  x  20  =  8.755. 
8.75      x  12  =  105d. 

ANALYSIS. — As  in  previous  example. 


Or, 


£  .4375 
20 

8.75005. 

12 

105.0000<1 


Ex.    Eeduce  T\  of  a  £  to  integers  of  lower  denominations,  i.e. 
to  shillings  and  pence. 


OPERATION. 


£  x  ¥  =  9rf. 

=  85.  96?. 


ANALYSIS.— Multiplying  by  20,  £T7g  =  8| 
shillings.  Reserve  the  integral  part  of  the 
result,  and  reduce  the  fractional  part  to  pence. 
Multiplying  by  12,  f  shilling  —  9  pence. 
Hence,  &fa  —  Ss.  9cf. 


Ex.    Eeduce  .4375  of  a  £  to  integers  of  lower  denominations. 


OPERATIONS. 

.4375  x  20  =  8.755. 


.75 


X  12  = 

Or, 

£.4375 
20 

5.8|.7500 

12 

d.  9|.0000 


ANALYSIS.— Multiplying  by  20,  £.4375  = 
8.75  shillings.  Reserve  the  integral  part  of 
the  result,  and  reduce  the  decimal  part  to 
pence.  Multiplying  by  12,  .75  shilling  = 
9  pence.  Hence,  £.4375  =  Ss,  9d. 


EXAMPLES. 


2O2.     1.  Eeduce  .625  of  a  £  to  pence. 

2.  Eeduce  .875  of  a  £  to  shillings  and  pence. 

3.  Eeduce  -^  of  a  £  to  pence. 

4.  Eeduce  -^  of  a  £  to  integers  of  lower  denominations. 

5.  Change  2.333^  yrs.  to  lower  denominations. 

6.  Change  £16.467  to  lower  denominations. 

7.  If   1  pound  sterling   can  be  bought  for  $4.87,  how  many 
pounds  can  be  bought  for  $10000  ? 

8.  Eeduce  2.417  yr.  to  lower  denominations. 


REDUCTION    OF    DENOMINATE    FRACTIONS.       69 

9.  A  cistern  is  16.25/2.  long,  9. 6 ft.  wide,  and  6.25  ft.  deep; 
what  is  its  capacity  in  cu.  yd.  etc.  ? 

10.  A  certain  sum  at  a  certain  rate  will  in  1  ?/r.  produce  $60 
interest ;  in  what  time  will  the  same  sum  at  the  same  rate  produce 
$15.50  interest  ? 

2O3.    To    reduce   denominate   numbers  to  fractions 
(or  decimals)  of  higher  denominations. 

Ex.     Reduce  f  of  a  penny  to  the  fraction  of  a  £. 

OPERATIONS.  ANALYSIS. — Divide  the  given  fraction 

3     •    i  9  _       t_  e  by  the  numbers  of  the  scale  required  to  re- 

"F    ~  -*•*  —    ¥o  *•  / 

j i_  on  i     n  duce  pence  to  pounds. 

If  the  answer  is  required  in  the  form  of 

^r?  -f  X  i^f  X  T^O"  —  -f-^-Q  £•       a  decimal,  reduce  the  resulting  fraction  to  a 
4  decimal  by  Art.  127.     £^  =  £.0025. 

Ex.  Reduce  .6  of  a  penny  to  the  decimal  of  a  £. 

OPERATION. 

•i  9  \    g    ,7  ANALYSIS. — As  in  previous  example. 

If  the  answer  is  required  in  the  form  of  a  fraction, 
reduce  the  resulting  decimal  to  a  fraction  by  Art.  131. 
£.0025  £.0025  =  £T^. 

Ex.     Change  9  pence  to  the  fraction  of  a  £. 

OPERATIONS.  ANALYSIS. — For  first  operation,  as  in  pre- 

t  v    i_  v    l-  —  JL  £        vious  examPle- 

T4*  '  Or,   since  there  are  240  pence  in   £1,  1 

Or    £    9     £  3_  penny  equals  ^¥  of  a  £,  and  9  pence  equal 

^  or  ^  of  a  £> 

Ex.    Reduce  9  pence  to  the  decimal  of  a  £. 

OPERATIONS. 

12  )9.          d. 

20  )  .75       s.  ANALYSIS. — As  in  previous  example. 

.0375  £. 

Ex.     Reduce  12s.  9d.  to  the  fraction  of  a  £. 

OPERATION. 

125.  9d.  =  153^.  ANALYSIS.— 12  shillings  9  pence  =  153  pence. 

£1  _  240^.       Since  £1  =  240  pence,  1  penny  equals  ^  of  a  £. 
and  153  pence  equal  £f  f ,  or  f  £  of  a  £. 

irrb"  —  •§?•  *• 


70  DENOMINATE     NUMBERS. 

Ex.    Reduce  £18  12s.  9d.  to  the  decimal  of  a  £. 

OPERATION.  ANALYSIS.  —  Write  the  denominations  given  in  a  verti- 

12  )     9.       d.       cal  column,  the  lowest  denomination  at  the  top.     Since 

20  )  12  75  S        tnere  are  12  pence  in  1  shilling,  9  pence  are  equal  to  .75 

shilling  ;   to  which  annexing  the  12  shillings  given,  we 

£18.6375       h^  13>75  shillings.     Since  there  20  shillings  in  £1,  12.75 

shillings  are  equal  to  £.6375,  to  which  annexing  the  £18, 

ive  have  £18.6375.    Hence  £18  12*.  9d.  =  £18.6375. 


EXAMPLES. 

*   2O4.     1.  Reduce  |  of  a  penny  to  the  fraction  of  a  pound. 
^  2.  Reduce  .875  of  a  shilling  to  pounds. 

3.  Change  12  cwt.  to  the  decimal  of  a  ton. 

4.  Reduce  420  grains  to  the  fraction  of  an  ounce  Troy. 
^  5.  Reduce  J  of  a  penny  to  the  decimal  of  a  pound. 

^  6.  What  part  of  a  mile  is  .165  of  a  foot  ? 
7.  What  decimal  of  a  £  are  18s.  6tl  ? 

NOTE.  —  The  following  method  for  reducing  shillings,  pence,  arid  farthings 
to  the  decimal  of  a  pound  is  sufficiently  accurate  for  most  business  purposes  : 
Write  one-half  of  the  greatest  even  number  of  shillings  as  tenths,  and  if  there 
be  an  odd  shilling  write  5  hundredths  ;  reduce  the  pence  and  farthings  to  far- 
things, and  write  their  number  as  thousandths.  If  the  number  of  farthings  is 
between  12  and  36,  add  1  to  the  thousandths  ;  if  between  36  and  48,  add  2  to  the 
thousandths.  Thus,  £8  17s.  Sd.  =  £8  +  £.85  +  £.033  =  £8.883. 

8.  Reduce  116  cu.ft.  to  the  decimal  of  a  cord. 

9.  Reduce  £247  14s.  Qd.  to  pounds. 

^  10.  What  decimal  of  an  acre  are  16  sq.  rds.  ? 

11.  Reduce  75  feet  to  the  fraction  of  a  mile. 

12.  Reduce  £27  105.  6d.  to  pounds. 

13.  What  is  the  cost  of  22480  pounds  of  coal  at  $4.25  per  ton 
(2240  pounds)  ? 

14.  What  is  the  cost  of  16  tons  12  cwt.  of  "Nut"  coal  at  &6.80 
per  ton,  and  8  tons  16  cwt.  of  "  Chestnut"  coal  at  $6.10  per  ton  ? 

15.  What  is  the  cost  of  8364  pounds  of  oats  at  $1.65  per  cental  ? 

16.  What  is  the  cost  of  8375  pounds  of  oats  at  $0.56  per 
bushel  ? 

17.  If  1  pound  is  equivalent  to  $4.8  7f  ,  what  is  the  value  of 
£1234  165.  9rf.  in  U.  S.  money  ? 

18.  Reduce  £25  12s.  Qd.  to  the  decimal  of  a  £,  and  multiply 
the  result  by  .05. 


ADDITION.  71 


ADDITION. 

205.  Denominate  numbers  are  added,  subtracted,  multiplied) 
and  divided  by  the  same  general"  methods  as  are  employed  for  like 
operations  in  abstract  numbers.     The  only  difference  arises  from 
the  use  of  a  varying  scale  instead  of  the  uniform  scale  of  10. 

Ex.     Add  £5  11s.  4=d.,  £7  14s.  9d.,  £6  16s.  Sd.,  and  £7  5s.  9£ 

OPERATION.  ANALYSIS.  —Write  the  numbers  so  that  like  denomina- 

£      s.       d.  tions  stand  in  the  same  column,  and  begin  to  add  at  the  right. 

5  11     4  The  sum  of  the  pence  is  3Qd.  =  2s.  Qd.   Write  the  Qd.  under 
7     14     9  the  column  of  pence,  and  add  the  2s.  to  the  column  of  shil- 

6  16     8  hn£s>  obtaining  for  the  sum  48*.  =  £2  8s.    Write  the  8$. 
-,               Q  under  the  column  of  shillings,  and  add  the  £2  to  the  column 

of  pounds,  obtaining  for  the  sum  £27 ;  which  write  under 

27        86       the  column  of  pounds,  producing  the  entire  sum,  £27  8*.  Qd. 

EXAMPLES. 

206.  1.  Add  £16  5s.  4&,  £12  8s.  9d,  £13  14s.  Sd.,  £42  Os.  7&, 

and  18s.  6d. 

2.  Add  3T.  IScivt.  2qr.  16  lb.,  4T7.  I3cwt.  3qr.  14/5.,  1ST. 
13  cwtf.  24  lb.,  and  42  T7.  8  c?<tf.  1  qr.  22  ft.  (Long  Ton  Table). 

3.  Add  £163  16s.  1167.,  £52  8s.  Qd.,  £3  14s.  2d.,  £84  12s.  lid., 
£106  Is.  4d,  and  £49  13s.  &Z. 

,£.  Add  1  yr.  6  mo.  10  da.,  3  ?/r.  8  mo.  24 da.,  kyr.  11  mo.  16  da., 
3  mo.  18  da.,  and  1  ?/r.  8  mo.  8  rfa. 

5.  Add  Scd.  WQcu.ft.,  3  cd.  Socu.ft.,  2  cd.  ll^cu.ft.,  and 
5ctf.  114  cu.ft. 

6.  Add  16  7^r.  43  min.  48  sec.,  3  hr.  12  mm.  40  sec.,  1  hr.  49  mw. 
13  sec.,  and  5  Ar.  19  sec. 

7.  Add  116°  32'  44",  8°  28'  53",  10°  44'  12",  and  16°  18'  13". 

8.  Add  12  ch.  13  I,  16  ch.  92  I,  83  e#.  5  ?.,  4.16  ch.,  and  5.05  c/z. 

9.  Add  1  $.  11  oz.  18  ^w#.  14  ^r.,  2  lb.  8  03.  10  pwt.,  4  /S.  5  0«. 
ISgr.,  and  10  00.  \3pivt.  12 gr. 

10.  Add  16^.  3^.  1^.,  4&gal.  2qt.,  11  gal.  Iqt.  Ipt.,  4: gal. 
3qt.,  15 gal.  Ipt.,  and  24 gal.  3qt.  Ipt. 

11.  Add  £17  16s.  Sd.,  £37  13s.  5d.,  £46  7^.,  £11  5s.  10&,  £8 
4s.,  £38  19s.  3d.,  and  £45  12s.  Sd. 

12.  Add  £175  14s.  M.,  £37  9s.  3rf.,  £5  10s.  9^.,  17s.  3<Z.,  £55 
17s.,  £3  6s.  9&,  £44  18s.  5d.,  £218  15s.  6d.,  and  £3  11s. 


72  DENOMINATE    NUMBERS. 

SUBTRACTION. 

2O7.     Ex.  From  £10  65.  4&  take  £8  15*.  3d 

OPERATION.  ANALYSTS.— Write  the  numbers  so  that  like  denomina- 

£       s.      d.  tions  stand  in  the  same  column,  and  begin  to  subtract  at  the 

10  6     4  right.     3d.  from  4d.  leaves  Id.,  which  write  under  the  col- 
8     15     3  unm  of  pence.     Since  15s.  cannot  be  subtracted  from  6s., 

~     —     7~      take  £1  =  20s.  from  £10,  leaving  £9,  and  add  it  to  the  6s., 
making  26s.     15s.  from  26s.  leaves  11s.,  which  write  under 
the  column  of  shillings.    £8  from  £9  leaves  £1,  which  write  under  the  column 
of  pounds.    Hence  the  difference  required  is  £1  lls.  Id. 

EXAMPLES. 

2OS.    1.  From  £175  165.  Sd.  take  £87  12s.  6£ 

2.  From  £84  105.  2d.  take  £63  5s.  lOd. 

3.  From  £16  6s.  lid.  take  £12  12s.  Sd. 

4.  From  £48  10s.  Sd.  take  £24  16s.  lOd. 

5.  From  16  yr.  8  mo.  10  da.  subtract  12  yr.  5  mo.  8  da. 

6.  From  1880  yr.  10  mo.  16  da.  take  1876  yr.  5  mo.  24=  da. 

7.  From  1881  yr.  4  mo.  25  da.  take  1880  yr.  10  mo.  15  da. 

8.  From  1882  yr.  3  mo.  20  </o.  take  1879  yr.  8  mo.  26  da. 

9.  From  8/ir.  16mm.  44  sec.  subtract  6Ar.  18mm.  40 se^. 

10.  From  105°  43'  12"  subtract  87°  49'  16". 

11.  From  18  T.  IGcwt.  3qr.  21lb.  take  IT.  2cwt.  2qr.  25  Ib. 
(Long  Ton  Table). 

2O9.  To  find  the  interval  of  time  between  two  dates. 

21.O.  There  are  two  methods  in  common  use  for  finding  the 
time  between  two  dates  :  1,  by  compound  subtraction,  in  which 
the  result  is  given  in  years,  months,  and  days,  and  in  which  12 
months  are  considered  a  year,  and  30  days  a  month  ;  2,  the  result 
is  given  in  days,  or  in  years  and  days,  and  the  true  number  of 
days  is  taken  for  each  month. 

Ex.    Find  the  time  in  months  and   days  from  Apr.  24  to 

Nov.  10. 

OPERATION.  ANALYSIS*— Represent  the  months  and  days  by  their  num- 

mo.    da.       foers  and  find  their  difference  by  compound  subtraction,  writing 

11  10       the  later  date  as  the  minuend  and  the  earlier  as  the  subtrahend. 
4     24  Tn  many  examples  the  interval  may  be  found  mentally  as 

~~I     T7       follows :  From  Apr.  24  to  Oct.  24  are  6  mo. ;  in  Oct.  there  are  6 
more  days  after  the  24th  (regarding  each  month  as  30  days), 


SUBTRACTION.  73 

and  in  November  to  Nov.  10th  inclusive,  there  are  10  days.  Hence  the  total 
time  between  the  given  dates  is  6  mo.  16  da. 

The  above  methods  may  be  used  for  finding  the  exact  interval  in  days  by 
making  the  necessary  corrections.  6  mo.  16  da.  =  196  da.  From  Apr.  24  to 
Nov.  10,  there  are  4  months  containing  31  da.  each ;  hence  the  true  answer  is 
196  da.  +  4  da.,  or  200  da. 

NOTE. — When  the  month  of  February  is  included,  subtract  2  days  in  a 
common  year,  and  1  day  in  a  leap  year. 

Ex.    Find  the  time  from  May  18,  1876,  to  Mar.  2,  1882. 

OPERATION. 

yr.     mo.    da. 

ANALYSIS.— As  in  preceding  example. 
1876     5     18 

5  ~9     14 

Ex.  What  is  the  exact  number  of  days  from  July  20,  1880, 
to  Nov.  10,  1881  ? 

OPERATION.  ANALYSIS.— In  finding 

360  from  July  20,  1880,  to  July  20,  1881.      the  interval  between  two 

11  remaining  in   July.  dates  the  last  day  is  count- 

31  in  August.  ed,  and  not  the  first.    Since 

30  in  September.  the  time  is  more  than  one 

31  in  October.  year'  write  down  365  days 
10  in  November.  as  the  number  of  days  from 

the  first  date  to  the  same 
478  from  July  20,  1880,  to  Nov.  10,  1881.  date  of  the  next  year.  Next 

write  down  the  number  of 

days  in  the  month  of  July  after  the  20th,  then  the  number  of  days  in  each 
of  the  full  calendar  months,  and  finally  the  number  of  days  in  November  to 
Nov.  10  inclusive.  The  sum  of  these  numbers  will  be  the  required  time. 

EXAMPLES. 
211.  Find  the  time  by  compound  subtraction  from 

1.  Jan.  10  to  Aug.  28. 

2.  Mar.  16  to  Dec.  4. 

3.  Feb.  5,  1880,  to  Oct.  16,  1881. 

4.  Jan.  27,  1881,  to  July  4,  1883. 

5.  May  16,  1882,  to  Mar.  24,  1884. 

6.  June  28,  1881,  to  Apr.  10,  1882. 

7.  July  30,  1882,  to  May  12,  1883. 

8.  Aug.  16,  1883,  to  Jan.  1,  1885. 

Find  also  the  exact  number  of  days  between  the  above  dates. 


74  DENOMINATE   NUMBERS. 

MULTIPLICATION. 

212.     Ex.  Multiply  £7  16*.  8d  by  11. 

OPERATION.  ANALYSIS. — 11  times  8d.  are  SSd.  =  Is.  4d.     Write  t&e 

£      s.      d.        4^  under  the  pence,  and  add  the  7s.  to  the  product  of  shil- 
7     16     8         lings.     11  times  16s.  are  176s.,  plus  7s.  from  the  preceding 
11         product  are  183s.  =  £9  3s.     Write  the  3s.  under  the  shil 
Z^       "^     2         lings,  and  add  the  £9  to  the  product  of  pounds.     11  times 
£7  are  £77,  plus  £9  from  the  preceding  product  are  £86, 
which  write  under  the  pounds.     Hence  the  entire  product  is  £86  3s.  4cJ. 

Ex.    Multiply  £8,12*.  6d.  by  .05. 

OPERATION. 

12)6.       d. 

20  )12.5       8.  ANALYSIS.— Reduce  the  multiplicand  to  the  deci- 

8.625  £        mal  of  a  pound  by  Art.  203,  perform  the  required  mul- 

_05  tiplication,  and  reduce  the  result  to  shillings  and  pence 

by  Art.  201. 
£  -43125  £8  i2s.  Qd.  =  £8.625 

20  £8.625  x  .05  =  £.43125 

s.  8.62500  £'43125  =  Ss-  7M- 

12 

d.  7.50000 

EXAMPLES. 

313.     1.  Multiply  £17  105.  Sd.  by  9  ;  by  11 ;  by  15. 

2.  How  many  cords  of  wood  in  12  loads,  each  load  containing 
2cd.  lOScu.ft.? 

3.  "What  is  the  cost  of  25  yd.  of  silk,  at  £1  2s.  Qd.  per  yd.  ? 

4.  What  is  .05  of  £127  165.  6d.  ?     Of  £145  15s.  U.  ? 

5.  "What  is  the  weight  of  24  silver  spoons,  each  spoon  weighing 
loz.  ISpwt.? 

6.  Multiply  1  hr.  38  min.  22  sec.  by  15  ;  by  12 ;  by  18. 

7.  If  15  men  perform  a  certain  piece  of  work  in  3  da.  16  hr. 
5% min.,  how  long  would  it  take  one  man  to  perform  it? 

8.  Multiply  £138  Ss.  9d.  by  .02| ;  by  .06  ;  by  .07. 

9.  What  will  50 gal  of  wine  cost  at  85.  3d.  per  gallon  ? 

10.  How  much  grain  in  12  bins,  each  containing  13  lu.  3  pic. 
6qt.? 

11.  If  a  man  walk  4:  mi.  3  fur.  32  rd.  in  one  hour,  how  far  will 
he  walk  in  10  hours  ?     In  16  hours? 


LONGITUDE     AND     TIME.  75 

DIVISION. 

214.  Ex.  If  6  yds.  of  cloth  are  worth  £8  18s.  6d.  what  is 
1  yd.  worth  ? 

OPERATION.  ANALYSIS. — lyd.  is  worth  1  sixth  as  much  as  Gyd. 

£      *•      d-        i  of  £8  is  £1  and  £2  remaining.     Write  the  £1  in  the 
6  )  8      18      6         quotient,  and  reduce  the  £2  to  shillings.     £2  —  40s.,  plus 
1        99        18s.  i*1  the  dividend  =  58s.     ^  of  58s.  is  9s.  and  4s.  re- 
maining.    Write  the  9s.  in  the  quotient,  and  reduce  the 
4s.  to  pence.     4s.  =  48d.,  plus  Qd.  in  the  dividend  =  54d.     $  of  54<2.  is  Sd.s 
which  write  in  the  quotient.     £1  9s.  9d.  is  the  quotient  required. 

NOTE. — When  the  divisor  is  a  denominate  number,  as  in  Ex.  2,  reduce 
both  divisor  and  dividend  to  the  same  denomination,  and  divide  as  in  simple 
numbers. 

EXAMPLES. 

j     215.     1.  Divide  £13  125.  3d.  by  11  ;  by  9  ;  by  33. 

J  2.  How  many  yards  of  muslin  at  Id.  per  yard  can  be  bought 
for  £5  12s.  ?    For  £9  9*.  ?     (See  note.) 
8.  Divide  Us.  3d.  by  .05  ;  by  .09 ;  by  .15. 

Reduce  the  dividend  to  the  decimal  of  a  pound,  then  divide  in  the  usual 
/manner,  and  reduce  the  quotient  to  pounds,  shillings,  and  pence. 

\j  4-  How  many  yards  of  silk  at  £1  19s.  2d.  per  yard  can  be  pur- 
chased for  £86  3s.  4rf.?     (See  note.) 

5.  Divide  85°  18'  30"  by  15  ;  by  18 ;  by  27. 

6.  If  48  shares  of  a  certain  stock  are  worth  £2013  8s.,  what  is 
the  value  of  1  share  ? 

V  7.  Divide  322  A.  90  sq.  rd.  by  10  ;  by  13  ;  by  16. 

8.  A  pile  of  wood  4=ff.  wide  and  6ft.  high  contains  18  cd. 
72  cu.  ft. ;  what  is  the  length  of  the  pile  ? 

9.  If  120   spoons  weigh  32  Ib.    9  oz.  15  piot.,   what  does   1 
weigh  ? 

\/10.  If  42  yd.  of  cloth  cost  £20  16s.  6df.,  what  is  the  price  of 
1  yd.  ?     Of  12  yd.  ?     Of  20  yd.  ? 

LONGITUDE    AND     TIME. 

216.  The  whole  circle  of  the  earth,  or  360°,  passes  under  the 
sun  in  24  hours,  and  in  1  hour  passes  -^  of  360°,  or  15° ;  in  1 
minute,  -g^  of  15°  (15  x  60'),  or  15' ;  and  in  1  second,  -^  of  15' 
(15  x  60"),  or  15". 


76 


DENOMINATE     NUMBERS. 


Comparison  of  Longitude  and  Time. 


For  a  difference  of 
15°   in  Longitude 
15'     " 
15"    " 

1°    "         "  ' 

I"    "        " 


There  is  a  difference  of 
1  hr.    in  Time. 
1  min.  "      " 
1  sec.    "      " 
4  min.  "      " 
4  sec.    "      " 

-&S6C.      "        " 


218.  RULE.  —  1.  The  difference  in  longitude  of  two  places, 
expressed  in  °  '  ",  divided  by  15  will  produce  their  differ- 
ence in  time  expressed  in  hours,  minutes,  and  seconds. 

2.  The  difference  in  time  of  two  places,  expressed  in 
hr.  min.  sec.,  multiplied  by  15  will  produce  their  difference 
in  longitude  expressed  in  °  ". 


219.    TABLE  OF  LONGITUDES. 


Albany 73° 

Ann  Arbor 80° 

Boston 71° 

Berlin   13° 

Calcutta 88° 

Cincinnati ,  84° 

Chicago 87° 

Jefferson  City,  Mo. . .  92° 

London 0° 

Mexico 99° 


44'  50"  W 

New  York 

74°    0'    3"  W. 

43'          W 

New  Orleans 

90°    2'  30"  W 

3'  30"  W.v 

Paris  

.     2°  20'  22"    E. 

23'  45"    E. 
19'    2"    E 

Philadelphia  

.  75°  10'           W. 
.  12°  27'  14"    E. 

29'  31"  W 

Richmond  Va  

.  77°  25'  45"  W. 

37'  45"  W 

San  Francisco 

122°  26'  45"  W. 

8'           W. 
5'  38"  W 

St.  Paul,  Minn  
St  Louis  Mo  .    .  . 

.  95°    4'  55"  W. 
.  90°  15'  15"  W 

5'          W. 

Washington,  D.  C. 

.  77°    0'  15"  W. 

EXAMPLES. 

22O.  Find  the  difference  in  longitude  between 

1.  New  York  and  London.  4>  St.  Louis  and  Calcutta. 

2.  Boston  and  Paris,  5.  Philadelphia  and  Berlin. 

3.  Chicago  and  San  Francisco.    6.  San  Francisco  and  Calcutta. 

Find  the  difference  in  time  between 

7.  New  York  and  Greenwich.    10.  Eome  and  London. 

8.  Chicago  and  New  York.        11.  Paris  and  Albany. 

9.  Kichmond  and  Calcutta.        12.  Calcutta  and  Jefferson  City. 


THE     METRIC     SYSTEM.  77 

13.  The  difference  in  time  between  New  York  and  Greenwich 
is  4  lir.  56  min.  %  sec. ;  what  is  the  difference  in  longitude  ?  When 
it  is  12  o'clock  noon  at  New  York,  what  is  the  time  at  Greenwich  ? 

14.  A  navigator  finds  that  when  it  is  noon  at  his  place  of 
observation,  it  is  16  min.  34  sec.  past  10  P.M.  by  his  chronometer, 
Greenwich  time  ;  what  is  his  longitude  ? 

15.  When  it  is  6  o'clock  P.M.  at  Richmond,  Va.,  what  is  the 
time  at  St,  Louis,  Mo.  ? 

16.  If  the   difference   of  time  between  two  places  is  1  7tr. 
IS  min.  4  sec.,  what  is  the  difference  of  longitude? 

17.  When  it  is  20  min.  past  2  P.M.  at  Boston,  Mass.,  what 
o'clock  is  it  at  San  Francisco  ? 

18.  When  it  is  9  o'clock  P.M.  in  San  Francisco,  it  is  3  min. 
3^  sec.  past  11  A.M.  in  Calcutta;  what  is  the  longitude  of  San 
Francisco,  if  the  longitude  of  Calcutta  is  88°  19'  2"  E.? 

19.  When  it  is  noon  in  Chicago,  it  is  5  min.  29^  sec.  of  1  P.M. 
in  New  York ;  what  is  the  longitude  of  Chicago,  the  longitude  of 
New  York  being  74°  3"  W.  ? 

THE    METRIC    SYSTEM. 

221.  In  the  Metric  System,  the  Meter  is  the  basis  of  all 
the  weights  and  measures  which  it  employs. 

222.  The  Meter  is  the  unit  of  length,  and  is  equal  to  one 
ten-millionth  part  of  the  distance  measured  on  a  meridian  of  the 
earth  from  the  equator  to  the  pole,  and  equals  about  39.37  inches. 

The  standard  meter  is  a  bar  of  platinum  carefully  preserved  at  Paris. 
Exact  copies  of  the  meter  and  the  other  units  have  been  procured  by  the 

*  The  use  of  the  metric  system  is  (1878)  obligatory  in  Belgium,  France,  Germany, 
Greece,  Netherlands,  Italy,  Portugal,  Roumania,  Spain,  and  Switzerland  ;  in  the  Argentine 
Republic,  Brazil,  Peru,  San  Domingo,  United  States  of  Colombia,  and  Uruguay— countries 
aggregating  a  population  of  181,000,000— while  its  use  is  partial  or  legalized  in  Austria, 
Azores,  Madeira  and  Cape  de  Verde  Islands,  Central  American  States,  Denmark,  Japan, 
Sweden,  Norway,  Turkey,  Spanish  Possessions,  Great  Britain  and  the  British  Possessions, 
and  our  own  country,  aggregating  a  population  of  375,000,000  more.  For  the  year  ending 
June  30,  1877,  the  value  of  our  imports  from  countries  where  the  metric  system  is  obligatory 
amounted  to  $177,807,4(59;  partially  in  use,  $17,378,785;  legalized,  $265,211,585;  not  legalized 
or  in  use,  only  $23,804,140.  Of  the  amount  received  from  countries  where  its  use  is  legalized, 
Great  Britain  and  British  Possessions  furnish  $185,667,400.  With  th/se  countries  our  present 
system  is  partly  in  harmony,  but  unfortunately  the  bulk  of  our  trade  with  them  is  made  up 
of  articles  measured  by  the  bushel  and  gallon,  neither  of  which  standards  corresponds  to 
any  bushel  or  gallon  of  this  country.  It  should  be  borne  in  nVlnd  that  the  only  legalized 
system  of  weights  and  measures  in  this  country  to-day  is  the  metric  system,  and  that  this 
system  is  the  only  one  we  possess  in  harmony  with  that  of  any  other  country. 


78 


DENOMINATE     NUMBERS. 


several  nations,  including  the  United  States,  that  have  legalized  the  system. 
Comparisons  with  the  standard  units  are  made  under  certain  conditions  of 
temperature  and  atmospheric  pressure. 

223.  The  names  of  the  higher  denominations,  or  multiples, 
of  the  unit  are  formed  by  prefixing  to  the  several  units  the  Greek 
numerals,  deka  (10),  hecto  (100),  kilo  (1000),  and  myria  (10000) ; 
as  dekameter,  10  meters,  hectometer,  100  meters,  etc. 

To  assist  the  memory,  observe  that  the  initial  letters  of  the  multiples  are 
in  alphabetical  order ;  thus,  D,  If,  K,  and  M. 

224.  The  names  of  the  lower  denominations,  or  divisions,  of 
the  unit  are  formed  by  prefixing  to  the  several  units  the  Latin 
numerals,  deci  (TV),  centi  (TOO)>  m^  (roW)  5   as  decimeter,  ^ 
meter,  centimeter,  -^  meter,  etc. 

To  assist  the  memory  observe  that  the  following  words  are  derived  from 
the  same  roots:  dime,  decimal,  decimate,  decennial,  etc.;  cent,  cental,  century, 
centennial,  etc.;  mill,  millennium,  etc. 


LINEAR    MEASURE. 
225.    TABLE. 


10  mm.  = 
10  cm.  = 

1  Millimeter. 
1  Centimeter. 
1  Decimeter 

•  •  •  '(woir  °f  a  meter) 
•  •  ••(T&U  °f  a  meter) 
(.jig.  of  a  meter) 

= 

.  03937  in. 
.3937m. 
3.937  in. 

10  dm.  = 

1  METER 

.  .  .  .(1  meter) 

_ 

39.37  in. 

10  w.  = 

10  Dm.  = 
10  Hm.  = 

1  Dekameter. 
1  Hektometer 
1  Kilometer.  . 

(10  meters) 
.  .  .  .(100  meters) 
....(1000  meters) 

= 

32.8/J. 
328.  09  /*. 
.62137  wit. 

NOTES. — 1.  The  meter,  like  the  yard,  is  used  in  measuring  cloths,  ribbons, 
laces,  short  distances,  etc. 

2.  The  kilometer  is  used  in  measuring  long  distances,  and  is  about  f  of  a 
mile. 

3.  The  centimeter  and  millimeter  are  used   by  artisans  and  others  in 
measuring  minute  lengtiis.     The  other  denominations  are  rarely  used. 

EXAMPLES. 

226.    1.  Eeduce  875275  meters  to  kilometers. 

ANALYSTS.— Since  1  kilometer  equals  1000  meters,  in  875275  meters  there 
are  as  many  kilometers  as  1000  is  contained  times  in  875275,  or  875.275.  To 
divide  by  1000  place  the  point  three  places  to  the  left  (143,  3). 

2.  Reduce  675.318  kilometers  to  meters. 

ANALYSIS.— Since  1  kilometer  equals  1000  meters,  in  675.318  kilometers 


THE    METRIC     SYSTEM.  79 

there  are  675.318  times  1000,  or  675318  meters.     To  multiply  by  1000,  place 
the  point  three  places  to  the  right  (14O,  note). 

3.  Keduce  383.64  meters  to  centimeters  ;  to  kilometers. 

4.  Keduce  175.16  centimeters  to  kilometers  ;  to  meters. 

5.  Reduce  to  meters  and  find  the  sum  of  876.2  decimeters, 
30347  centimeters,  176.48  meters,  8.175  kilometers. 

6.  A  ship  sails  5712  kilometers  in  48  days  ;  how  many  kilo- 
meters does  she  sail  per  day? 

7.  What  is  the  value  of  56.4  meters  of  silk  at  $1.75  per  meter  ? 

8.  16  pieces  of  cloth  contain  38.5  meters  each  ;  18  pieces  con- 
tain 39  meters  each;  and  24  pieces  contain  41.2  meters  each; 
how  many  meters  in  all  ? 

9.  How  many  meters  of  ribbon  at  27  cents  per  meter  can  be 
purchased  for  $245.70  ? 

SQUARE    MEASURE. 

227.  The  unit  of  square  measure  is  the  square  meter. 

TABLE. 

100  Square  Centimeters,  sq.  cm.  =  1  Square  Decimeter  =  15.5+  sq.  in. 

tOO  Square  Decimeters,  sq.  dm.  =  1  SQUARE  METER,  Sq.  M.  =  1.196+  sq.yd. 

NOTES. — 1.  The  square  meter  is  used  in  measuring  flooring,  ceilings,  etc.; 
the  square  decimeter  and  the  square  centimeter  are  used  for  minute  surfaces. 

2.  Since  units  of  square  measure  form  a  scale  of  hundreds,  each  denomi- 
nation must  have  two  places  of  figures. 

228.  The  unit  of  Land  Measure  is  the  are,  and  is  equal 
to  a  square  dekameter  (100  square  meters),  or  119.6  square  yards. 

TABLE. 

1  Centare.  ..(1  square  meter)  =  1550  sq.  in. 

100  Centares,  ca.  =  1  Are (100  square  meters)      =  119.6  sq.  yd. 

100  Ares,        A.  =  1  Hectare.  ..(10000  square  meters)  =  2.471  acres. 

NOTE. — The  hectare  is  the  ordinary  unit  for  land. 
EXAMPLES. 

229.  1.  Write  16  sq.  m.,   8  sq.  dm.,   24  sq.  cm.,  having  the 
square  meter  as  the  unit.  Ans.  16.0824. 

2.  Write  83  sq.  m.,  9  sq.  dm.,  having  the  sq.  m.  as  the  unit. 


80  DENOMINATE     NUMBERS. 

3.  In  47  ares  how  many  square  meters  ? 
4-  In  60.25  hectares  how  many  centares? 

5.  How  many  square  meters  in  a  building  lot  8  m.  by  32  m.? 

6.  How  many  building  lots,  each  containing  225  sg.  m.,  can  be 
formed  from  a  field  containing  9  hectares  ? 

7.  How  many  hectares  in  a  farm  1.024  Km.  in  width  and 
1.625/iw?.  in  length? 

8.  AVhat  is  the  cost  of  a  mirror  2.25m.  by  1.44?^.,  at  $3.84 
per  s^.  m.  ? 

9.  How  many  lots  25  m.  wide  by  60  m.  deep,   or  haying  an 
equivalent  area,  can  be  laid  out  from  6  hectares  ? 

10.  A  man  bought  a  piece  of  land  for  $6950.50,  and  sold  it  for 
87603.30,  by  which  transaction  he  made  $6.80  a  hectare;  how 
many  hectares  were  there  ? 

11.  If  the  forward  wheels  of  a  carriage  are  3.5  meters  in  cir- 
cumference, and  the  hind  weels   4.8  meters,   how  many  more 
times  will  the  forward  wheels  revolve  than  the  hind  wheels,  in 
running  a  distance  of  8.4  kilometers? 


CUBIC    MEASURE. 

230.  The  unit  for  measuring  ordinary  solids  is  the  cubic 
meter. 

TABLE. 

1000  Cu.  Millimeters,  cu.  mm.   =  1  Cu.  Centimeter  =     .061  eu.  in. 
1000  Cu.  Centimeters,  cu.  cm.   =  1  Cu.  Decimeter     =     61. 027  cu.in. 

1000  Cu.  Decimeters,   cu.  dm.  =  1  Cu.  METER         =  J35-317  cu-fL 

ll. 808  CM.  yd. 

NOTES. — 1.  The  cubic  meter  is  used  in  measuring  embankments,  excava- 
tions, etc.;  cubic  centimeters  and  cubic  millimeters  for  minute  bodies. 

2.  Since  units'  of  cubic  measure  form  a  scale  of  thousands,  each  denomi- 
nation must  have  three  places  of  figures. 

231.  The  unit  of  "Wood  Measure  is  the  ster,  and  is  equal 
to  a  cubic  meter,  or  35.317  cubic  feet. 

TABLE. 

10  Decisters,  da.  =  1  Ster. .  .  .(1  Cubic  Meter)     =  \  '3759  cord' 

(  35. 317  eu.  ft. 

10  Sters,  ,9.  =  1  Dekaster,  Ds.  .(10  Cubic  Meters)  =     2.759  cords. 


APPROXIMATE    RULES. 


85 


8.  In  5000  U.  S.  bushels,  how  many  hectoliters  ?     How  many 
dekaliters  ? 

9.  In  875  cu.  yd.  how  many  cu.  m.  ? 

10.  In  1000  cu.  m.  how  many  cu.  yd.  ? 

11.  Reduce  1728  gal.  wine  to  liters  ;  to  dekaliters, 

12.  In  244  sq.  m.  how  many  sq.  yd.  ?     How  many  sq.  ft.  ? 

13.  Reduce  220  oz.  Av.  to  grams  ;  to  kilograms. 

24O.    APPROXIMATE  VALUES. 

When  no  great  accuracy  is  required,  we  may,  for  all  practical  purposes, 
consider — 


1  decimeter        =  4  inches. 

1  cu.  met.  or  ster  =  l£  cu.  yd.,  or  \  cord. 

1  meter               —  39  inches. 

1  liter                    =  1  quart. 

5  meters              =  1  rod. 

1  hectoliter           =  2|  bushels. 

1  kilometer         =  f-  mile. 

1  gram                   =  15£  grains. 

1  square  meter  =  lOf  square  feet. 

1  kilogram            =  2i  pounds. 

1  hectare             =  2|  acres. 

1  ton                      ~  2200  pounds. 

APPROXIMATE     RULES. 

241.  To  reduce  avoirdupois  ounces  to  grams : 

Multiply  by  SO,  and  then  deduct  one-twentieth  (5  per  cent.). 
NOTE.— Answer  too  great  by  about  5g.  for  every  1000 #.  of  the  result. 

242.  To  reduce  avoirdupois  pounds  to  kilograms : 

Divide  ~by  2,  and  then  deduct  one-tenth. 

NOTE. — Answer  too  small  by  about  8  kilos  for  every  1000  kilos  of  the 
result.  If  -/y,  instead  of  y1^,  be  deducted,  the  answer  will  be  too  great  by  2 
kilos  for  every  1000  kilos  of  the  result. 

243.  To  reduce  avoirdupois  pounds  to  half-kilograms, 
or  German  pounds  : 

Deduct  one-tenth. 

NOTE. — The  answer  by  this  rule  will  be  too  small  by  about  8  German 
pounds  for  every  1000  German  pounds  of  the  result.  If  -^  be  deducted,  the 
answer  will  be  too  great  by  2  German  pounds  for  every  1000  German  pounds 
of  the  result. 

244.  To  reduce  tons  (2000  Ibs.)  to  metric  tons  : 

Deduct  one-tenth. 

NOTE. — The  same  relative  error  as  in  Art.  242. 


86  DENOMINATE    NUMBERS. 

245.  To  reduce  yards  to  meters : 

Deduct  one-twelfth. 

NOTE. — Answer  too  great  by  2J  m.  for  every  1000m.  of  the  result. 

246.  To  reduce  square  yards  to  square  meters  : 

Deduct  one-sixth. 

NOTE. — Answer  too  small  by  about  3  sq.  m.  for  every  1000  sq.  m.  of  the 
result. 

247.  To  reduce  cubic  yards  to  cubic  meters : 
Divide  by  1.3. 

NOTE. — Answer  too  great  by  about  6  CM.  m.  for  every  1000  CM.  m.  ot  the 
result. 

248.  To  reduce  U.  S.  gallons  to  liters : 

Multiply  by  4)  and  then  subtract  one-twentieth  (5  per  cent.). 
NOTE. — Answer  too  great  by  about  4Z.  for  every  1000?.  of  the  result. 

249.  To  reduce  U.  S.  bushels  to  hectoliters : 

Divide  by  3,  and  then  add  one-twentieth  (5  per  cent.). 

NOTE. — Answer  too  small  by  about  Ihl.  for  every  1000 hi.  of  the  result. 

250.  To  reduce  grams  to  avoirdupois  ounces : 

Divide  by  30,  and  then  add  one-twentieth  (5  per  cent.). 
NOTE. — Answer  too  small  by  about  8  ounces  for  every  1000  ounces  of  tLa 
result. 

251.  To  reduce  kilograms  to  avoirdupois  pounds: 

Multiply  by  2,  and  then  add  one-tenth. 

NOTE. — Answer  too  small  by  about  2  ll\  av.  for  every  1000  Ib.  av.  of  the 
result. 

252.  To  reduce  German  pounds,  or  half-kilograms, 
to  avoirdupois  pounds  : 

Add  one-tenth. 

NOTE. — Same  error  as  in  Art.  251. 

253.  To  reduce  metric  tons  to  U.  S.  tons  (2000  Ibs.) : 
Add  one-tenth. 

NOTE.— Answer  too  small  by  about  2  TJ.  S.  tons  for  every  1000  tons  of  the 
result. 


APPROXIMATE     RULES.  87 

254.  To  reduce  meters  to  yards  : 

Add  one-twelfth,  and  1%  of  the  original  number. 

NOTE.—  Answer  will  be  too  small  by  only  \  yd.  for  every  1000#d  of  the 
result. 

This  method  is  used  at  the  New  York  Custom  House  and  is  sufficiently 
accurate  for  practical  purposes. 

If  -^  be  added,  the  answer  will  be  too  small  by  about  2^  yd.  for  every  1000 
yd  of  the  result.  If  ^  be  added,  the  answer  will  be  too  great  by  about  6  yd. 
for  every  IQWyd.  of  the  result. 


Ex.    According  to  above  rule,  how  many  yards  in  324  meters  ? 
(Exact  result  is  354.  33  yd.    Error  only  .  09  yd.  ) 


OPERATION. 

324 


255.  To  reduce  square  meters  to  square  yards  : 

Add  one-fifth. 

NOTE.  —  Answer  too  great  by  about  3  sq.  yd.  for  every  1000  sq.  yd.  of  the 

result. 

256.  To  reduce  cubic  meters  to  cubic  yards  : 

Multiply  by  1.3. 

NOTE.  —  Answer  too  small  by  about  6  cu.  yd.  for  every  1000  cu.  yd.  of  the 
result. 

257.  To  reduce  liters  to  U.  S.  gallons  : 

Multiply  by  2.11,  and  then  divide  by  8. 

NOTE.  —  Answer  too  small  by  about  1.7  gal.  for  every  1000  gal.  of  the  result. 

Ex.    In  144  liters,  how  many  U.  S.  gallons  ? 

OPERATION. 

144 
144 
288  (Exact  result  should  be  38.04.    Error  only  .06  gal. 


8 )  303.84 
37.98 

258.  To  reduce  hectoliters  to  U.  S.  bushels. 

Multiply  by  3,  and  then  subtract  one-twentieth  (o  per  cent.). 
NOTE.— Answer  too  great  by  about  46w.  for  every  1000  Zw.  of  the  result. 


88 


DENOMINATE    NUMBERS. 


259.     FOREIGN    WEIGHTS    AND     MEASURES. 


ARGENTINE  CONFEDERATION. 

Metric  system  used  in  the  assess- 
ment of  duties.  Old  Spanish  weights 
and  measures  (see  Spain)  in  common 
use. 

AUSTRIA,  (AS  GERMANY.) 
BELGIUM,  (METRIC  SYSTEM.) 

BOLIVIA. 

The  metric  system  is  the  legal  sys- 
tem, but  the  law  has  not  been  rigidly 
enforced.  Old  Spanish  weights  and 
measures  (see  Spain)  still  in  use.  For 
coin  weight  the  metric  gram  is  used. 

BRAZIL,  (METRIC  SYSTEM.) 
Diamonds  are  permitted  to  be  sold 

according  to  the  old  Portuguese  outava 

(55.34  grains). 

Ships'   freights,  are,   for    the  most 

part,  settled  according  to  the  English 

ton  (2240  ».). 

CANADA,  (AS  GREAT  BRITAIN.) 

CAPE  OF  GOOD  HOPE,  (AS  GREAT 
BRITAIN.) 

CEYLON,  (AS  GREAT  BRITAIN.) 

CHILI,  (AS  BOLIVIA.) 
For  custom   purposes,  the   metric 
system  is  enforced. 


CHINA. 

ITael 
1  Catty 
1  Picul 
1  Chih 

=     \\oz.  av. 
=     l£ft.  a  v. 
=     133'-  ft-  av. 
=     14.1  inches. 

1  Chang 

=     11.75  feet. 

COLUMBIA,  (METRIC  SYSTEM.) 


DENMARK. 

1  Pound  (I  kilogram)  =  1.102  ft.  av. 

1  Centner  (100ft.) 

1  Tonde  of  grain 

1  Tonde  of  coal 

1  Fod  (Foot) 

1  Viertal 

1  Alen  (Ell) 


=  110.23ft.  av. 

=  3.948  U.S.&M. 

=  4.825  U.S.&M. 

=  1.03  U.S.  ft. 

=  2.04  U.S.  gal. 

=  .6864yd 

Coinage  laws  are  metric.  The  in- 
troduction of  complete  metric  system 
is  in  prospect. 

ECUADOR,  (METRIC  SYSTEM.) 
ENGLAND,  (SEE  GREAT  BRITAIN.) 
EGYPT,  (METRIC  SYSTEM.) 

FRANCE,  (METRIC  SYSTEM.) 
The  old  French  aune  =  45  inches 
is  still  used  to  some  extent  in  the  silk 
industries  of  France  and  the  U.  S. 

GERMANY. 

Metric  system  with  a  few  changes 
in  subdivisions  in  general  use. 
1  Pound  (i  kilogram)   =  1.1023ft.  av. 
1  Centner  (100  pounds)  =  110.23ft.  av. 
1  Wispel  (metric  ton)  =  2204.6  ft.  av. 

GREAT  BRITAIN. 

Imp.  Gallon  =  1.2  U.S.  gal 

"     Bushel  =1.03U.S.Zw. 

"     Quarter  =  8.25  U.S.  bu. 

Ale  or  Beer  Gallon  =  1.22  U.S.  gal. 
Cental  =  100  ft. 

Quarter  of  Wheat  )       AQn  77 
at  London  f  ~        ' lb' 

1  Quarter  of  Wheat  at  Hull )   _  Kn4  „ 

and  Newcastle.  f  ~ 

1  Quarter  of  Wheat  at  Dnn- )   _  AQR  „ 
dee  and  other  places.       f  ~ 

Metric  system  permitted  by  law  of 
1864. 


FOREIGN     WEIGHTS     AND     MEASURES. 


89 


GREECE. 

Metric  system  with  the  common 
Grecian  names  in  general  usa. 

In  the  Ionian  Islands  the  English 
weights  and  measures  have  been 
legalized  since  1829. 

HONG  KONG,  (AS  CHINA.) 

INDIA. 

1  Seer  =  16  chattacks. 
1  Bombay  Maund  of  40  seers  —28  Ib.&v. 
1  "         42    "     =29.4  " 

1  Surat  "         40    "     =31£    " 

1      "  "42    "     =391  « 

1      "  "44    "     =41Ty< 

1  Bengal  Factory  Maund  =74|  " 
1  "  Bazaar  "  =82$  " 
1  Madras  Maund  =25  " 

!Bom'yCandyof20niaunds=560  " 
1  Surat  "  "  "  =746|" 

1  Madras  "  "  M  =500  " 
1  Travancore"  "  "  =660  " 
1  Tola  =180$r. 

1  Guz  of  Bengal  =  1  Eng.  yard. 

1  Corge  =20  units. 

1  Corge  Pound  =20  Ib. 

Metric  system  permissive. 

ITALY. 

1  Palm  =  .555  cu.  ft. 
Metric  system  in  general  use. 

JAPAN. 

1  Picul  =  133  i  Ib.  av. 
For  coinage,  in  part,  the  metric  unit 
of  weight  is  used. 

JAVA. 

1  Amsterdam  Pond  =  1.09  #>.  av. 
1  Picul  =  133^    " 

1  Catty  =  li        " 

1  Chang  =  4  yards. 

LIBERIA. 

British  weights  and  measures  gen- 
erally used. 


MEXICO. 

Weights  and  measures  are  legally 
the  metric,  but  the  metric  system  is 
not  generally  in  force,  the  old  Spanish 
weights  and  measures  (see  Spain)  being 
still  employed. 

NETHERLANDS. 

Metric  system   with    a   change  in 
names  in  general  use. 
1  Last  (30  hectoliters)  =  85.134  bu. 

NORWAY  AND  SWEDEN. 
1  Swedish  Skalpond  =    0.93^  Ib.  av. 
1  Swedish  Centner     =    93£ 
1  Norwegian  Fund     =     1.1 
1  Swedish  Fot  =     11.7  inches. 

1  Norwegian  Fod       =     12.02     " 

In  Norway  the  metric  system  is  used 
to  some  extent. 

In  Sweden,  the  coin  weight  and  the 
medicinal  and  apothecary  weight  are 
metric.  The  complete  metric  system 
is  now  permissive,  and  will  be  obliga- 
tory after  1882. 

PERU,  (AS  BOLIVIA.) 

PORTUGAL. 
Metric  system  compulsory  since  Oct. 


1, 

The  chief  old  measures  are — 
1  Libra  =  1.012  Ib.  av. 

1  Almunde  of  Lisbon  =  4.42  U.  S.  gal. 
1  Alquiere  =  .3928  U.  S.  bu. 

RUSSIA. 

1  Pound  =  0.9  Ib.  av. 

1  Pood  (63  to  a  ton)  =  36     " 
1  Berkowitz  =  360    " 

1  Chetvert  -=  5.956  U.S.&w. 

1  Vedro  =  3.25  U.  S.  gal. 

1  Arsheen  =  28  inches. 

1  Ship  Last  =  2  tons. 

Metric  system  partially  in  use. 

SIAM. 

1  Tael  =  li  oz.  av. 
Picul,  Catty,  and  Chang,  same  as  Java. 


90 


DENOMINATE     NUMBERS. 


SPAIN,  (METRIC  SYSTEM.) 

In  many  of  the  South  American 
States  and  in  Cuba,  the  old  Spanish 
weights  and  measures,  principally 
Castilian,  are  used.  They  are  as  fol- 
lows : 

1  Libra  =  1.014  Ib.  av. 

1  Arroba  (25  Libras)  -  25.36  " 
1  Quintal  (100  Libras)  =  101.44  " 
1  Vara  -  .914  yd. 


SWITZERLAND. 

Metric  system  used  with  some 
changes  of  names  and  subdivisions. 
Pure  metric  system  optional. 

TURKEY,  (METRIC  SYSTEM.) 

URUGUAY,  (AS  ARGENTINE  CONFED- 
ERATION.) 

VENEZUELA,  (METRIC  SYSTEM.) 


REVIEW    EXAMPLES. 

26O.  1.  How  many  days  from  Mar.  1C  to  Oct.  4  ?  From 
June  30  to  Dec.  25  ? 

2.  Find  the  time  by  compound  subtraction  from  Aug.  23, 
1882,  to  Jan.  15,  1884. 

3.  How  many  leap  years  from  1881  to  1897  ?    From  1795  to 
1845  ?    From  1889  to  1909  ? 

4.  Reduce  2.375  years  to  years,  months,  and  days. 

5.  Suppose  a  person's  income  to  be  $1000  per  day,  how  much 
is  that  per  minute  ? 

6.  How  many  chains  in  one  mile  ? 

7.  In  4376  feet  how  many  chains  ?    How  many  inches  ? 

8.  In  396  rods,  how  many  chains  ?    How  many  feet  ? 

9.  In  37.56  chains,  how  many  feet  ?     How  many  rods  ? 

10.  Children's  size  1  of  shoemakers'  measure  is  4£  inches  long ; 
what  is  the  length  of  boys'  size  8,  youths'  size  1,  and  men's  size 
10  ?  (Size  1  of  the  second  series  is  one  size  longer  than  size  13  of 
the  first  series.  See  Art.  157.) 

11.  How  many  square  feet  in  a  rectangular  lot,  whose  breadth 
is  25f  feet  and  whose  length  is  116 \  feet  ? 

12.  How  many  square  feet  in  a  lot  25  feet  front  and  100  feet 
deep? 

IS.  How  many  acres  in  a  rectangular  field,  28.50  chains  by 
46.38  chains  ? 

14*  How  many  acres  in  a  rectangular  piece  of  land,  224  links 
by  448  links  ? 

15.  How  many  acres  in  a  square  lot  whose  side  is  31 6 £  links  ? 
208. 71  feet? 

16.  How  many  square  yards  in  a  floor,  16ft.  6  in.  by  12ft. 


REVIEW    EXAMPLES.  91 

17.  How  much  will  it  cost  to  carpet  a  floor  16ft.  by  18/i!f.,  with 
carpeting  f  yd.  wide,  at  $1. 60  per  yard  ? 

18.  What  is  the  value  of  a  field  320  rd.  long  and  160  rd.  wide 
at  $22.50  an  acre? 

19.  A  rectangular  lot  contains  24  acres  ;  what  is  its  width,  its 
length  being  1056  feet  ? 

20.  How  much  will  it  cost  to  dig  a  cellar  36  ft.  long,  30  ft. 
wide,  and  6  ft.  deep,  at  30  cents  per  cubic  yard  ? 

21.  If  a  pile  of  bark  is  40  ft.  long  and  4 ft.  wide,  how  high 
must  it  be  to  contain  10  cords  ? 

22.  How  many  feet,  board  measure,  in  16  boards  each  IS  ft. 
long,  10  in.  wide,  and  1  in.  thick  ? 

23.  How  many  feet,  board  measure,  in  12  planks,  each  10  ft. 
long,  12  in.  wide,  and  2  in.  thick  ? 

££.  How  many  board  feet  in  225  cubic  feet  ? 

25.  What  is  a  pile  of  wood,  19/2.  long,  ll//.  5  iw.  high,  and 
8/tf.  7m.  broad,  worth,  at  $5.62£  per  cord? 

26.  Paid  $222.75  for  boards  at  $13.50  per  M.;  how  many  feet 
were  purchased  ? 

27.  What  is  the  value  of  27315  ft.  of  lumber  at  $12  per  M.  ? 

28.  How  many  pills,  each  containing  5  grains,  can  be  made 
from  1  Ib.  av.  of  quinine  ? 

29.  In  70  oz.  Tr.,  how  many  oz.  av.? 

30.  In  70 II.  Tr.,  how  many  Ib.  av.  ? 

5^.  What  is  the  cost  of  11  T.  12  cwt.  of  "Nut"  coal  at  $6.95 
per  ton,  and  9  T.  16  cwt.  of  "Chestnut"  coal  at  $6.25  per  ton? 

32.  What  is  the  freight  of  16  T.  17  cwt.  25  Ib.  at  $5  per  ton 
(2240  Ib.)  ? 

33.  What  is  the  cost  of  15669  pounds  meal  at  $1.10  per  cwt.? 

34.  What  cost  16450  pounds  of  hay  at  $15.50  per  ton? 

35.  In  27318  pounds  of  corn,  how  many  bushels  ?    What  is 
the  value  of  the  same  at  48|-  cents  per  bushel  ? 

36.  What  is  the  value  of  27318  pounds  of  corn,  at  87.1  cents 
per  cental  ? 

NOTE. — Examples  35  and  36  illustrate  the  present  and  the  cental  systems 
of  buying  and  selling  produce,  and  show  the  calculations  saved  by  using  the 
latter. 

37.  In  7346  pounds  of  oats,  how  many  bushels  ? 

38.  What  is  the  cost  of  273-Jj-  bu.  oats,  at  58  c.  per  bushel  ? 

39.  What  is  the  value  of  281  Ib.  peas  at  $1.05  per  bushel  ? 


92  DENOMINATE     NUMBERS. 

40.  What  is  the  value  of  291  Ib.  of  peas  at  $1.75  per  cental  ? 

41.  What  is  the  value  of  186  Ib.  of  beans  at  $2.25  per  bushel  ? 

42.  Wk'.t  is  the  cost  of  192  Ib.  of  beans  at  $3.75  per  cental  ? 

43.  At  what  price  per  bushel  is  rye  at  $1.227  per  cental? 
Oats  at  $1.66  per  cental?    Barley  at  $2.126  per  cental  ?    Malt  at 
$2.75  percental  ? 

44-  How  many  bushels  in  27316  pounds  of  wheat?  In  24375 
pounds  of  corn  ?  In  16218  pounds  of  oats  ?  In  21412  pounds  of 
barley?  In  17387  pounds  of  malt? 

45.  How  many  bushels  in  54  centals  of  wheat  ?    In  87  centals 
of  corn  ?     In  46  centals  of  oats  ?    In  53  centals  of  barley  ?    In  67 
centals  of  malt  ? 

46.  How  much  per  cental,  is  wheat  at  $1.85J  per  bushel? 
Corn  at  76J-  cents  per  bushel  ?    Oats  at  48}  cents  per  bushel  ?    Bar- 
ley at  87  cents  per  bushel  ? 

47.  How  much  per  bushel  is  wheat  at  $1.27  per  cental  ?    Corn 
at  $1.323  percental? 

48.  How  much  per  cental  is  timothy  seed  at  $1.75  per  bushel  ? 
Clover  seed  at  $8. 55  per  bushel  ? 

49.  What  is  the  cost  of  56123  bushels  oats  at  43  cents  per 
bushel  ?    Of  41 114  bushels  corn  at  46  cents  per  bushel  ? 

50.  A  quartermaster  purchased  75000  pounds  of  corn,  at  31} 
cents  per  bushel ;  32113  pounds  of  oats,  at  32^  cents  per  bushel ; 
and  79500  pounds  of  hay,  at  $22.37£  per  ton  (2000  pounds).  What 
was  the  total  cost  of  the  purchase  ? 

51.  A  farmer  sold  18360  pounds  of  corn,  art  64  cents  per  cen- 
tal ;   22450  pounds  of  oats,  at  94  cents  per  cental  ;   and  36650 
pounds  of  hay,  at  $1.31  per  cental.    How  much  was  realized  from 
the  sale  ? 

52.  How  many  sheets  of  paper  in  5  reams  ? 

53.  When  1  gold  dollar  was  worth  $2.85  in  currency,  what 
was  the  value  of  the  legal  tender  dollar  in  gold  ? 

54.  How  many  grains  of  gold  and  alloy  respectively  are  re- 
quired for  the  coinage  of  6983  gold  dollars  ? 

55.  How  many  Troy  ounces  of  pure  silver  would  be  required 
in  the  coinage  of  2,000,000  standard  silver  dollars  ?    How  much 
copper  ? 

56.  What  is  the  avoirdupois  weight  of  100000  double-eagles, 
25000  eagles,  1000  half-eagles,  4000  quarter-eagles,  and  1983  gold 
dollars  ? 


REVIEW    EXAMPLES.  93 

57.  What  is  the  value  of  an  oz.  Tr.  of  standard  gold,  making 
no  allowance  for  the  alloy  and  coinage  ?     Of  an  oz.  av.  ? 

58.  What  is  the  value  of  an  oz.  Tr.  of  pure  gold,  making  no 
allowance  for  the  alloy  and  coinage  ?     Of  an  oz.  av.  ? 

59.  Feb.  26,  1879,  the  Nevada  Bank  of  San  Francisco  sold 
100,000  ounces  of  pure  silver  to  the  United  States,  at  $1.08£  per 
ounce.    At  this  rate,  what  is  the  intrinsic  gold  value  of  the  stand- 
ard silver  dollar  ? 

60.  The  coinage  at  the  mints  of  the  United  States  during  the 
fiscal  year  ending  June  30,  1879,  was  as  follows  : 

GOLD— Double-eagles,  $57,234,340;  eagles,  $1,03.1,440;  half- 
eagles,  $1,442,130;  three  -  dollars,  $109,182;  quarter-eagles, 
$1,166,800;  dollars,  $3,020  ;  total  gold,  $ . 

SILVER— Dollars,  $27,227,050;  Half-dollars,  $225;  quarter- 
dollars,  $112.50  ;  dimes,  $45;  total  silver,  $ . 

MINOR    COINAGE  —  5-cents,    $1,175;    3-cents,    $984;     cents, 
$95,639  ;  total  minor  coinage,  $ . 

How  many  pieces  were  coined  and  what  was  the  total  value  of 
the  coinage  ? 

61.  Add  £27  16s.  10c?.,  £6  10s.  8d.,  £47  15s.  lid.,  £25  7s.  U., 
£3  14s.  8^.,  and  £23  16s.  3d. 

62.  In  47  guineas,  how  many  shillings  and  pounds  ? 

68.  What  is  the  value  of  45000  tons  of  steel  rails  at  97s.  6d. 
per  ton  ?  What  is  the  value  per  ton  in  U.  S.  money  ?  Of  total 
in  U.  S.  money  ? 

64.  How  many  yards  of  cloth  at  3s.  6d.  per  yard  can  be  bought 
for  £7  ? 

65.  Beduce  £19  16s.  3d.  to  the  decimal  of  a  pound. 

66.  If  £1  sterling  is  worth  $4.87,  what  is  the  value  of  £225 
18s.  Qd.  ? 

67.  From  £16  12s.  9d.  deduct  .05  of  itself. 

68.  What  is  the  value  of  20  yd.  silk  at  10s.  Qd.  per  yard  ? 

69.  If  1  franc  is  worth  $.193,  what  is  the  value  of  $1  in  francs  ? 

70.  What  is  the  value  in  U.  S.  money  of  875  Napoleons? 
(1  Napoleon  =  20  francs.) 

71.  What  is  the  cost  of  50  meters  silk  at  8.25  francs  (8  francs 
25  centimes)  per  meter  ? 

72.  What  is  the  value  in  U.  S.  money  of  24000  marks? 

73.  What  is  the  value  in  U.  S.  money  of  5,528,364  Brazilian 
reis  ?     Of  7387  Portuguese  mi^-eis  ? 


94  DENOMINATE     NUMBERS. 

74.  In  8375  pies   (money  of  India),  how  many  annas  and 
rupees  ? 

75.  What  is  the  value  in  dollars  of  500  Eussian  poods  of  rye 
at  75  copecks  per  pood  ? 

76.  The  gold  yen  of  Japan  contains  1£  grams  of  fine  gold  and 
weighs  If  grams.    What  is  its  fineness,  and  what  is  its  intrinsic 
value  compared  with  the  U.  S.  gold  dollar  ?     How  many  yens  can 
be  coined  from  10  grams  of  Japanese  standard  gold  ? 

77.  The  difference  in  the  local  time  of  two  places  is  3hr. 
43  min.  12  sec. ;  what  is  the  difference  in  longitude  ? 

78.  When  it  is  4  hr.  40  min.  A.M.  at  Chicago,  what  is  the  time 
at  Calcutta? 

79.  How  many  bushels  will  a  box  10  ft.  long,  5  ft.  wide,  and 
4  ft.  high  contain  ? 

NOTE.— Since  a  bushel  is  about  l£  cubic  feet,  the  following  approximate 
rules  may  be  used  for  all  practical  purposes  : 

To  reduce  cubic  feet  to  bushels :    Deduct  one-fifth. 

The  result  will  be  too  small  by  about  4£  bushels  for  every  1000  bushels  of 
the  result. 

To  reduce  bushels  to  cubic  feet :    Add  one-fourth. 

The  result  will  be  too  great  by  about  4£  cubic  feet  for  every  1000  cubic 
feet  of  the  result. 

Solve  the  above  example,  both  exactly  and  approximately,  and  compare 
the  results. 

80.  How  many  hectoliters  of  grain  will  a  box  4  meters  long, 
3.2  meters  wide,  and  2.5  meters  high  contain  ? 

81.  How  many  gallons  of  water  will  a  cistern  hold  which  is 
Sft.  long,  7  ft.  wide,  and  10  ft.  deep? 

82.  What  is  the  capacity  in  liters  of  a  cistern  25  meters  long, 
2.2  meters  wide,  and  3  meters  deep  ? 

88.  In  52  meters  cassimere,  how  many  yards  ? 

84.  The  specific  duty  on  Brussels  carpet  is  44  cents  per  square 
yard  ;  what  is  the  duty  per  square  meter  ? 

85.  In  a  pane  of  glass  24  in.  by  30  in.,  how  many  square  deci- 
meters ? 

86.  The  duty  on  pig-iron  is  $7  per  ton  (2240  Ib.) ;  what  is  the 
duty  per  metric  ton  or  millier  ? 

87.  The  U.  S.  custom  duty  on  alcohol  is  $2  per  gallon  ;  what 
is  the  duty  per  liter  ? 

88.  The  duty  on  tallow  candles  is  2£  cents  per  pound;  what 
is  the  duty  per  kilogram  ? 


PERCENTAGE. 


261.  Percentage  is  a  term  applied  to  all  operations  in 
which  100  is  used  as  the  basis  of  computation. 

It  is  also  the  name  given  to  any  number  of  hundred ths  of  a  number. 

262.  Per  Cent.  (%}  is  an  abbreviation  of  the  Latin  per 
centum,  meaning  on  or  by  the  hundred. 

Thus,  5%  means  5  of  every  hundred,  or  5  hundredths  (Tf  P,  or  .05). 

263.  Any  per  cent,  may  be  expressed  in  the  form  of  a  decimal 
or  fraction. 

Thus  5  per  cent.  =  5%  =  5  hundredths  =  .05  —  Tf ^  =  ^.    The  first  two 
forms  are  used  in  the  statements  of  questions ;  the  others  in  the  operations. 

264.  In  percentage,  three  elements  are  considered,  viz  :  the 
Base,  the  Rate,  and  the  Percentage.     Any  two  being  given,  the 
other  can  be  found. 

265.  The  Percentage  is  the  result  obtained  by  taking  a 
certain  number  of  hundredths  of  a  number. 

266.  The  Base  is  the  number  of  which  a  certain  number  of 
hundredths  are  taken. 

267.  The  Rate  is  the  number  of  hundredths,  or  the  num- 
ber per  cent. 

Thus,  in  the  statement,  Q%  of  300  is  18,  the  Percentage  is  18,  the  Base 
300,  and  6  per  cent.  (.06)  is  the  Rate. 

268.  Applications  of  Percentage. — The  principles  of  per- 
centage are  applied  to  many  of  the  most  common  business  trans- 
actions.   Among  the  most  important  of  these  are  Trade  Discounts, 
Commission,  Insurance,  Profit  and  Loss,  Duties,  Interest,  and 
Exchange. 


96  PERCENTAGE. 

269.  Ex.  What  is  5  per  cent,  of  300  ? 

OPERATION.  ANALYSIS.— 5%  is  equivalent  to  5  hundred ths  (^,  or 

300  Base.  .05).     5  hundredths  of  a  number  may  be  found  by  mul- 

.05  Rate.  ti plying  it  by  5  hundredths.     For  convenience,  the  raul- 

"  tiplication  is  performed  by  expressing  the  5  hundredths 

in  the  form  of  a  decimal.     .05  x  300  =  15,  the  percentage 

required.     Therefore,  the  Percentage  is  the  product  of  two  factors,  the  Base 

and  the  Rate. 

Or,  \%  of  300  is  3,  and  5^  is  5  times  3,  or  15. 

Ex.     15  is  5  per  cent,  of  what  number  ? 

OPERATION.  ANALYSIS. — In  this  example  there  is  given  the  Per- 

Rate.  Percentage.       centage  and  Rate,  to  find  the  Base.    Since  the  Percentage^ 
.05  )  15.00  tbe  Base  x  tlie  Rate?  tlie  Bage  _  tiie  Percentage  -r-  the 

Base.   300.  Rate. 

Or,  if  15  is  5%  of  a  certain  number,  1  %  is  \  of  15,  or 
3  ;  and  the  number,  or  100% ,  is  100  times  3,  or  300. 

Ex.    15  is  what  per  cent,  of  300  ? 

OPERATION.  ANALYSIS. — The  Base  and  Percentage  are  given, 

Base.  Percentage.  Rate.       to  find  the  Rate      gince  the  percentage  =  the  Base 
300  )  15.00  (  .05         x  t]ie  Rate,  the  Rate  =  the  Percentage  -=-  the  Base 

15  -5-  300  =  .05  (5fo\  the  required  per  cent. 
Or,  15  is  aVv  or  ^  of  300.    ^  =  Tf  ^  or  5# . 

Ex.    What  is  4^  of  £247  13s.  Qd.  ? 

ANALYSIS. — Multiply  the  number  of  each  denom- 
ination by  .04,  as  in  the  margin,  and  then  reduce  the 
/c47     lo  decimal  parts  to  integers  of  lower  denominations 

.04          (201). 

£  91  88     52     24  ^r'  re(^uce  shillings  and  pence  to  the  decimal  of 

a  pound    (see  note,  Ex.  7,  Art.  204),  take  the  re- 
quired per  cent.,  and  reduce  the  decimal  result  to 
S.  18J.12  lower  denominations.     Thus, 

12  £247  13*.  Qd.  =  £247.675 

d  T~68  £247.675  x  .04  =  £9.907  =  £9  18s.  1.68& 

270.  These  principles  may  be  expressed  by  the  following 
formulae  : 

P  =  B  x  R\   B  =  P  -r-  R;   R  =  P  -f-  B. 

271.  EULES. — 1.    To  find  the  percentage,  multiply  the 
base  by  the  rate  expressed  decimally. 


PERCENTAGE.  97 

2.  To  find  the  base,  divide  the  percentage  by  the  rate 
expressed  decimally. 

3.  To  fi1^d  the  rate,  divide  the  percentage  by  the  base. 

NOTE.  —  In  finding  the  rate,  to  produce  a  quotient  of  hundredths,  make 
the  decimal  places  of  the  dividend  exceed  those  of  the  divisor  by  2. 

272.  When  the  rate  is  an  aliquot  part  of  100,  it  is  generally 
more  convenient  to  use  the  equivalent  fraction.     Thus, 

50%  =  .50    =  f  16|%  =  ,16f  =  f  6J%  =  .06J  =  TV 

33#£=  .33^  =  i  12i%  =  .121  =  i-  ^    =  .05    =  fr. 

25%  =  .25    =  \.  10%    =  .10    =  ^  3£%  =  .034  =  A- 

20%   -  -20    =  f  8J% 


EXAM  PLES. 

273.  What  is  Find 

7.  J  of  1728  ?  6.  16%  of  $375. 

2.  -fa  of  2456  ?  7.  8%  of  $24.25. 

5.  .25  of  5280  ?  &  2£%  (i  of  10  %)  of  876. 

4.  25%  of  8424?  9.   7  \%  (10%—  J  of  10%)  of  $1678. 

5.  \%  of  1000  ?  10.  l%(\%-  ^%)  of  $21275. 

11.  What  is  the  difference  between  2J%  of  $16000  and  5%  of 
$8475  ? 

./#.  A  merchant  bought  goods  amounting  to  $375.60,  and  sold 
them  so  as  to  gain  30%  of  the  cost  ;  how  much  did  he  gain  ? 

13.  A  lawyer  collected  $2875,  and  charged  5%  for  his  services  ; 
how  much  did  he  retain  for  his  services,  and  how  much  did  he 
pay  over  ? 

lit.  What  is  the  duty  on  twelve  watches  valued  at  $75  each,  at 
25%  of  the  value? 

15.  Jan.  10,  a  merchant  buys  a  bill  of  goods  amounting  to 
$876.40  on  the  following  terms  :  4  months,  or  less  5%  if  paid  in 
10  days.     How  much  would  settle  the  bill  Jan.  18  ? 

16.  The  product  of  two  factors  is  75  ;  if  one  of  the  factors  is 
.03,  what  is  the  other  factor  ? 

17.  The  percentage  is  60,  and  the  rate  2J%  ;  what  is  the  base  ? 

18.  $18.08  are  5%  of  what  ?  22.  165/2.  are  33£%  of  what? 

19.  $324  are  3%  of  what?  23.  £240  are  3£%  of  what  ? 

20.  $37.56  are  2J-%  of  what  ?  24.  $12.25  are  6£%  of  what  ? 

21.  $17.28  are  24%  of  what  ?  25.   96  francs  are  £%  of  what? 

7 


98  PERCENTAGE. 

26.  An  agent  sells  a  house  and  lot  for  $16450,  and  receives  5$ 
for  his  services ;  what  does  he  pay  to  the  owner  of  the  property  ? 

;  27.  Mr.  A  invests  42$  of  his  capital  in  real  estate,  and  has 
$53070  left ;  what  is  his  capital? 

28.  If  a  man  fails  to  pay  his  tax  until  he  is  charged  8$  addi- 
tional, how  much  will  he  lose  if  his  tax  is  $36.75? 

29.  If  the  rate  is  20$  and  the  percentage  440,  what  is  the 
base? 

80.  A  has  35$  of  his  property  invested  in  stocks,  10$  in 
horses  and  cattle,  18$  in  grain,  and  the  remainder,  which  is 
$24235,  in  real  estate.  What  is  the  total  value  of  his  property  ? 

31.  A  merchant,  failing  in  business,  pays  43$  of  his  indebted- 
ness ;  he  owes  A  $3750,  and  B  $6280 ;  how  much  does  he  pay 
each? 

82.  The  product  of  two  numbers  is  375  ;  if  one  of  the  numbers 
is  30000,  what  is  the  other  number  ?    Express  answer  in  hun- 
dredths. 

83.  The  assets  of  a  bankrupt  are  $27387,  and  his  liabilities 
$82161 ;  what  %  of  his  indebtedness  can  he  pay? 

What  per  cent,  of 

84.  375  is  75  ?  38.  $1000  is  $12.50  ? 
35.  $1728  is  $144?  39.  $3720  is  $232.50  ? 

86.  $3456  is  $72  ?  40.  $2416  is  $60.40? 

87.  5280  ft.  is  165  ft.  ?  41.  $1484  is  $21.20  ? 

i    42.  A  merchant  paid  for  goods  $345  and  sold  them  for  $258.75 ; 
the  loss  is  what  %  of  the  cost  ? 

48.  If  a  paymaster  receives  $150000  from  the  treasury,  and 
fails  to  account  for  $225  thereof,  what  is  the  percentage  of  loss  to 
the  government  ? 

44-  Total  imports  and  exports  carried  in  foreign  vessels  during 
the  fiscal  year  1858,  were  valued  at  $160,666,267 ;  in  American 
vessels  for  the  same  time,  $447,191,304.  What  per  cent,  were 
carried  in  American  vessels  ?  In  foreign  vessels  ? 

J  4-5-  $640  being  increased  by  a  certain  %  of  itself  equals  $720  ; 
required  the  rate  %. 

46.  A  commission  merchant  sold  450  barrels  of  flour  at  $5.30 
per  barrel ;  how  much  should  he  send  to  the  miller,  if  he  charges 
2£  per  cent,  for  making  the  sale  ? 


PERCENTAGE.  99 

47.  A  horse  was  sold  for  $658,  which  was  16f$  more  than  it 
cost ;  what  was  the  cost  ? 

NOTE.— The  cost  of  the  horse  was  f°$,  or  100%  of  itself  ;  since  the  gain 
was  \§\%  of  the  cost,  the  selling  price  (the  cost  plus  the  gain)  was  116f  $ 
of  the  cost.  $658  is  116f  ^  of  what  number? 

What  number  increased  by         "What  number  decreased  by 

48.  25%  of  itself  is  500  ?  51.  5%  of  itself  is  $307.80  ? 

49.  8%  of  itself  is  $1004.40  ?        62.  40$  of  itself  is  3726  ? 
60.  125%  of  itself  is  999  ?  68.  25%  of  itself  is  $342.60  ? 

54-  When  the  premium  on  gold  was  17f$,  what  amount  of 
gold  was  it  necessary  to  sell  to  pay  a  note  of  $3000  in  currency  ? 

55.  What  is  116$  of  1200  ? 

56.  144  is  120$  of  what  number  ? 
51.  375  is  what  $  of  300? 

68.  Find  95$  of  $1260. 

69.  Of  what  number  is  275,  100$  ? 

60.  $187.50  are  2J$  of  what  ? 

61.  Total  imports  and  exports  carried  in  foreign  vessels  for  the 
fiscal  year,  1879,  were  valued  at  $911,269,232;  in  American  ves- 
sels for  the  same  time,  $272,015,697.    What  per  cent,  were  carried 
in  American  vessels  ? 

62.  The  total  tonnage  entered  at  ports  of  the  United  States 
during  the  year  ended  June  30,  1879,  was  13,768,137  tons.     What 
per  cent,  was  entered  at  the  port  of  New  York  ?    (See  Ex.  64.) 

63.  The  tonnage  entered  at  the  four  ports  of  New  York, 
Baltimore,  Philadelphia,  and  Boston,  for  the  year  ended  June  30, 
1879,  was  10,489,660  tons.     This  amount  constituted  what  per 
cent,  of  the  total  tonnage  entered  at  ports  of  the  United  States  ? 
(See  Ex.  62.) 

64.  The  total  tonnage  entered  at  New  York  during  the  year 
ended  June  30,  1878,  was  5,545,026  tons ;  during  the  year  ended 
June  30,  1879,  6,661,825  tons.     What  was  the  increase  per  cent.  ? 

65.  The  earnings  of  the  Chesapeake  and  Ohio  B.R.  Co.  for 
the  month  of  July,  1878,  were  $14,026,189  ;   for  the  month  of 
July,  1879,  $17,338,273.    What  was  the  per  cent,  of  increase  ? 

66.  Find  5%  of  £375.  69.  Find  10$  of  £37  8s.  9tZ. 

67.  Find  2£$  of  £64  16s.  70.  16s.  is  2£$  of  what  ? 

68.  Find  4^  of  £75  12s.  Qd.       71.  £1  8s.  4rf.  is  4$  of  what  ? 


100  PERCENTAGE. 


DISCOUNTS. 

274.  It  is  customary  in  many  branches  of  business  for  manu- 
facturers and  dealers  to  have  fixed  price-lists  of  certain  kinds  of 
merchandise  ;  and  when  the  value  changes,  instead  of  changing  a 
long  price-list,  the  rate  of  discount  is  changed.    The  fixed  price 
is   called  the  List-Price,  and  the   discount  allowed  the  Trade 
Discount. 

Books  are  usually  sold  by  publishers  and  jobbers  at  certain  discounts  from 
the  retail  prices. 

275.  Many  kinds  of  merchandise  are  sold  at  "time"  prices, 
subject  to  certain  rates  of  discount  if  paid  at  an  earlier  period. 

1.  Thus,  the  following  or  similar  announcements  are  usually  found  upon 
the  bill-heads  of  wholesale  dealers  :  u  Terms,  4  months,  or  30  days,  less  5$"  ; 
or,  "  Terms  60  days,  or  1$  discount  in  30  days,  or  2$  discount  in  10  days." 

2.  In  the  same  business  house,  certain  goods  are  sold  on  long  credit,  and 
others  on  short  credit. 

3.  When  no  rate  of  discount  has  been  offered,  merchants  are  generally 
willing,  when  bills  are  paid  before  maturity,  to  deduct  the  interest  on  the 
amount  of  the  bill  for  the  remainder  of  the  time  at  the  legal  rate  per  annum. 

Ex.    The  list-price  of  a  scale  is  $80 ;  what  is  the  net  price  if 
a  discount  of  25%  and  10%  is  allowed? 

OPERATION. 

$80  List-price.  ANALYSIS. — The  first   rate  of  discount  is  reckoned 

20  25$ ,  or  4.       upon,  and  deducted  from  the  list-price,  and  the  others  are 
—  deducted  from  the  successive  remainders. 

The  result  is  not  affected  by  the  order  in  which  the 
_6  10$,  or  ^  discounts  are  taken.  A  discount  of  25$  and  10$  is  the 
54  Net-price  same  as  a  discount  of  10$  and  25$. 

EXAMPLES. 

276.  1.  The  gross  amount  of  a  bill  of  shoes  is  $82.68.   What 
is  the  net  amount,  the  rate  of  discount  being  5%  ? 

2.  A  stove  is  sold  for  $45  less  30%  ;  required  the  net  price  ? 

NOTE.— If  the  discount  is  not  required,  multiply  by  .70  (100$  — 30$); 
the  product  will  be  the  net  price. 

3.  What  is  the  value  of  466  Ib.  0.  W.  casing  @  45  cts.  per  pound, 
less  1-J  per  cent.  ? 


DISCOUNTS.  101 

4.  The  gross  amount  of  a  bill  of  mdse.  is  $106.36;  what  is 
the  net  amount,  the  rates  of  discount  being  20  %  and  10  $  ? 

5.  The  gross  amount  of  a  bill  of  notions  is  $49.75  ;  what  is  the 
net  amount,  the  rates  of  discount  being  10  $  and  10  $  ? 

6.  What  is  the  value  of  12  pair  shoes  @  $1.60  per  pair,  less  5  $  ? 

7.  What  direct  discount  is  equivalent  to  a  discount  of  15  % 
and  10$  ?    45$  and  10$  ?     20$  and  12£$  ?    60$  and  10$  ?     75$ 
and  12^$  ? 

8.  What  is  the  net  value  of  one  case  prints  containing  2273  yd., 
@-  4s  cts.,  less  5$,  cooperage  25  cts.  ? 

9.  A  bill  of  merchandise  amounting  to  $442.38  was  bought 
Aug.  18,  1879,  on  the  following  time  :  "  4  months  or  5$  off  30 
days."     How  much  would  settle  the  bill  Sept.  16,  1879  ? 

10.  What  is   the   net  value  of  a  bill  of  iron  amounting  to 
$1103.75,  at  a  discount  of  45,  10,  and  2  per  cent.? 

11.  What  is  the  net  value  of  1  case  prints  containing  30392?/(7. 
@  5  cts.  per  yd.,  less  a  discount  of  3$  ;  cooperage  $.25  ? 

12.  The  net  amount  of  a  bill  of  files  was  $36. 75  ;   what  was 
the  gross  amount,  the  rate  of  discount  being  10$  ? 

18.  Mr.  A.  is  offered  dress  goods  at  26°  cts.  per  yd.,  "  4  months, 
or  less  6$  cash  ";  how  many  yards  can  he  purchase  for  $49.82  ? 

14.  The  net  amount  of  a  bill  of  hardware  is  $175.26  ;  what  is 
the  gross  amount,  the  rate  of  discount  being  45$  and  10$  ? 

15.  What  is  the  difference  on  a  bill  of  $875  between  a  discount 
of  40$  and  a  discount  of  30$  and  10$  ? 

16.  A  bill  of  tinware  is  sold  at  the  following  discounts :  $74.20 
at  20$  and  10$;    $43.75  at  40$  and  5$  ;   $69  at  %?>\%  and  10$  ; 
and  $49.17  net.     What  is  the  total  net  amount  of  the  bill  ? 

17.  A  bill  of  dry  goods  amounting  to  $914.37  is  sold,  Aug.  19, 
on  the  following  terms :    "  60  days,  or  less  1$  if  paid  in  30  days, 
or  less  2$  if  paid  in  10  days."     How  much  would  settle  the  bill 
Sept.  18  ?     How  much  Aug.  27  ? 

18.  Of  a  bill  of  hardware,  $61.51  are  sold  at  a  discount  of  60 
and  5$;    $18.75  at  a  discount  of  10$;    $16.86  at  a  discount  of 
124$;   $44.25  at  a  discount  of  40  and  5$ ;  $29.60  at  a  discount 
of  40,  12J,  and  10$  ;    $28.04  at  a  discount  of  55^  ;   $16  at  a  dis- 
count of  65,  10,  and  10$  ;    $18.70  at  a  discount  of  50$  ;   $19.75 
at  a  discount  of  20$;  $18.50  at  a  discount  of  15$  ;   $307.55  at  a 
discount  of  75  and  12|$;    $36.61  at  a  discount  of  60  and  10$ ; 
and  $218.25  net.    What  is  the  total  net  amount  of  the  bill  ? 


102 


PERC  ENTA  GE. 


BILLS.* 

A  Bill  is  a  detailed  statement  of  merchandise  sold,  or 
of  services  rendered.  Bills  of  merchandise  state  the  place  and 
date  of  the  sale,  the  names  of  the  buyer  and  seller,  the  terms  of 
the  sale,  the  quantity,  price,  and  distinguishing  marks  and  num- 
bers of  the  merchandise,  and  other  details. 

The  terms  Bill  and  Invoice  are  used  by  many  interchangeably.  The  term 
Invoice  is  applied  more  particularly  to  statements  rendered  by  consignees  to 
commission  merchants,  showing  marks,  numbers,  values,  and  accrued  charges 
of  goods  shipped;  to  bills  rendered  to  jobbers  ;  and  to  bills  received  from  for- 
eign countries. 

EXAMPLES. 
278.  Copy  and  extend  the  following  bills  : 

(1.  Canned  Goods.) 
Folio  316.  WILMINGTON,  DEL.,  Nov.  16, 1876. 

Messrs.  WM.  DOLTON  &  Co., 

Bought  of  JAMES  MORROW  &  SON. 


Cases. 


Doz. 


3  Ib.  Peaches    -    -     -     -    - 

2  "     Saco  Corn      -     -    -     - 
2 1  "    Salmon     -     - 

3  "    Tomatoes,  B.  &  L.  -     - 
2| "    Col.  Pears     -    -    -    - 
2 1  "    Apricots 

Ctge. 


225. 
185 
385 

1*0 

4aa 
4  Q.O 


00 


50 


(2.  Flour.) 

BUFFALO,  N.  Y.,  Dec.  6,  1880. 
Messrs.  DANIEL  GROUSE  &  SONS, 

Bought  of  SCHOELLKOPP  &  MATTHEWS. 
Interest  charged  on  all  accounts  after  30  days.    We  allow  no  Expressage  or  Exchange. 


20 
25 

Bbls.  Flour  "  Sunlight  "  Sacks    -  $7.05 
Bbls.    -     7.25 

*** 
*** 

** 
** 

25 

"     "  Victor  "  Sacks    -     -     6.05 

*** 

** 

25 

Bbls.     -     -     625 

*** 

** 

15 

"      "  Dakota  "  Sacks  -    -     5.30 

#* 

•5s"S 

5 

"      "Superlative"  Sacks    8.55 

#* 

•X-Jfr 

20  bags 
70     " 

9177  Ih    ^    Mpal                                             120 

** 
*** 

** 

*** 

** 

264  92-  bu  Oats     .56 

*  For  explanation  of  marks,  numbers,  abbreviations,  etc.,  used  in  the  bills  of  this 
chapter,  see  page  312. 


BILLS. 


103 


BARK  ENTERPRISE, 

Terms  Cash. 


(3.  Storage,  etc.) 

BROOKLYN,  N.  Y.,  Jan.  30, 1879. 

To  J.  P.  &  G.  C.  ROBINSON,  Dr. 


Storage     

1631923 

bu.     @       %? 

122 

39 

Elevating     -     -    -     - 

163  1923 

@    w 

** 

** 

Delivering     -     -     -     - 

1631923 

@    yj' 

*# 

•X-* 

Weighing     -     -    -    - 
Carting    -     -     -     -     - 

1631923 
1631923 

@    %? 
@     i? 

** 
**# 

** 

Loading  ship    -     -     - 
Separating  damage    - 

1630134 
1630134 

per  M.  $7^ 

@    y^ 

*** 

^ 

Blowing  on  delivery  - 

1630134 

@       #f 

** 

** 

Weighing  on     " 

1630134 

@    y^ 

** 

** 

*** 

** 

(4.   Provisions.) 

CLEVELAND,  0.,  Oct.  9,  1876. 
Messrs.  L.  C.  MAGAW  &  SON, 

Bought  of  J.  P.  HOBISON  &  Co. 

Terms  Cash.— No  goods  sold  on  30  days. 


10 

"Rhlsi    S    M    Pork                                             17°° 

#** 

"       MPS<^  Bppf                                                1075 

** 

"     Hams        90a1376b^98c     ****d    14? 
"     Shoulders  58     744  -57        ***       9? 
"     Dr.  Beef    33     241  -22        ***     14? 
Tc.  Lard                    406  -60       ***     11? 

*** 
** 

** 

*** 

a  Number  of  pieces.    b  Gross  weight.    c  Tare,  or  weight  of  barrel  or  tierce.    d  Net  weight. 


(5.  Fish.) 

GLOUCESTER,  MASS.,  Sept.  28,  1876. 
Messrs.  DANIEL  WEIDMAN  &  Co., 

Bought  of  CLARK  &  SOMES. 

Subject  to  sight  draft  without  notice  after  thirty  days. 


0 

Of!    NPW  GPO   Cod                                         ^  7*1 

** 

** 

1 

Bbl  Ex  8  1  Mackerel                            20  00 

** 

** 

10 
10 
2 
10 
5 
3 

Kits  15  Ibs.  Ex.  *1  Mackerel  -     -     -     1.80 
"    201bs.  Bay  81       "          -    -    -    1.80 
Bbls.  jf  2  Shore              "        Ig.    -    -  12.00 
Kits  20  Ibs.  82  Shore   "         "     -    -    1.50 
Halfs  New  Labrador  Herring  -    -    -    3.82 
"      Round  Shore         "         -    -    -    2.95 
Box  >38,  ctg.  in  Boston  -90 

** 
** 
** 
** 
** 
* 
# 

** 
*•# 
** 
** 
** 
** 
** 

$*** 

*# 

104 


PER  CENT  A  GE. 


(6.  Groceries.) 


Order  Book,  410-22. 
Day  Book,  115-797. 

Messrs.  EDWARDS  &  Co., 


Terms  Cash  30  days. 
Shipped  per  National  Line. 


NEW  YORK,  Feb.  1, 1880. 


of  H.  K.  &  F.  B.  THURBER  &  Co. 


When  you  desire  to  order  goods,  same  as  had  before,  give 
date  of  purchase,  and  the  Order  and  Day  Book  pages. 


MCP#4385 

1 
3 
3 
4 
1 
2 
25 
10 

1 
1 

Cask  Old  Prunes  1544  -  134  = 

****  Ibs.  - 

4f 

165 
glO 
1»5 

.39 

.65 
.16 

l"o 

.25 
.25 

** 
* 
* 
* 
* 
* 
* 

4Ht 

* 
-X- 
1 
#** 

#-x 
** 
*# 
•** 
** 
** 

15 

"          "     Layer 
Cream  Tartar,  \  foil     - 
Yeast-Cakes,  3  doz.  ea., 
Ibs.  Whole  Pepper  .... 

-  20  Ibs.  - 
-    6  doz.  •• 

Box  0.  K.  Mustard,  }'s     -     - 

i's     -     - 
Cartage 

Bag      - 
-  12  Ibs.  - 
-  12  "     - 
on  all  -     - 

(7.  Groceries.) 


Messrs.  HORTON,  CRARY  &  Co., 


NEW  YORK,  Aug.  13,  1876. 


Bought  of  AUSTIN,  NICHOLS  &  Co. 


W.  B. 

1 

Bag  -20  Rio  Coffee  132     23 

30 

56 

A  Jf99 

1 

"     *80         "            ......     131     2l£ 

** 

*•* 

1 

Bbl/25  Roa.  Java  Coffee           *|}  -    100    25| 

** 

** 

2 

"    -50      ..       Rio          «     112-22221*       £&     04' 

Ml 

** 

H.  R.  P. 

1 

109—20    42  " 
Case  Cone.  Lye   ($.    -     - 

5 

50 

Union. 

2 

Boxes  Yeast  Cakes,  ea.  3            -     -       V    65 

* 

A.  N.  &  Co. 

25 
5 
1 

Ibs.  Spice,              Bag  20^     -    -  jk  *    -    15.  V 
Mats  Cassia    vL*HL"  .»  21|  26' 
Keo-  Gr  Mustard     -                               50    35 

* 
* 

#* 
** 
** 

10 

lbs°  White  Glue      ....  .,-,;£-     -    -    40 

# 

257-20  *;J* 

A.  N.  &  Co. 

5 

Bbls.  X.  C.  Sugar  -     -  StS  -^ 

SI-io     v  «4?  n| 

»** 

** 

$134 

1 

"     W.  D.  Syrup  ...     .    4^        ***  60 

** 

** 

$114 

1 

"    C.  D.      "         ....    4^        ***  50 

** 

** 

Ctg.  2-    -    - 

1 

50 

Syrup,     60  days    -    -    **.** 

$*** 

** 

Balance,  30    "       -    -  ***** 

SMMHI 

BILL  Si 


105 


(8.  Dry  Goods.) 

NEW  YORK,  March  20,  1879. 
Messrs.  FIELD,  LETTER  &  Co., 

Bought  of  H.  B.  CLAFLIN  &  Co. 

Terms  Cash  in  30  days  less  5£,  or  4  months'  note  delivered  within  30  days,  and  payable  at 
Bank  in  New  York  exchange. 


2875 
8039 
3369 
1290 
1590 


2179 
2507 
6515 
2985 
1650 


Bale  Boott  M.  Brown 

"     Continental  C.  do. 

"     Pequot  A.  36  in. 

"     Great  Falls  E.     -----     - 

"     Atlantic  H.     -     -     -   1038     -  .073 
Less  4$     - 


"    Boott  F.  F. 

"    Pepperell  600  Drill       -     -     - 
Case  Blackstone  A.  A.     .... 

"     Dwight  Anchor 

"     Great  Falls  Q.          .... 

"  Pearl  River  Ticking  -  -  - 

Cooperage 


800 

800 

967 

1111 

$** 


800 

622 

1649 

1139 

1492 

708 


071 
073 
071 
09 
08 
152 


54 

VV7T 


75 


Messrs.  DAVIDGE,  LANDFIELD  &  Co., 


(9.  Dry  G-oods.) 

NEW  YORK,  March  23,  1878. 


Bought  of  TEFFT,  GRISWOLD  &  Co. 


2 

Naumkeag  Bl.  Jean     •     -    Jy  -     -     - 

95 

09 

8 

55 

4 

Roll  Cambric           -     -     -  (SvS  '    " 

###* 

052 

* 

** 

,47s 

3 

Pprmprpll  T)rill                              '  3ft3 

**** 

08 

* 

** 

1 

T  nwAll    1  0  /     "RTnvvn 

38 

142 

* 

** 

.              1  p                                1  40 

*** 

07'2 

* 

on  men  a                           ^ 

V  I 

5 

i45s/45 
New  Market  N.       -     -     -  /45JW1 

*#«* 

06' 

** 

« 

2 

Champion  Cheviot       -     -  (  ^i  -     -     • 

MH 

09 

* 

...» 

2 

Otis  B.  B.  Dk  Stripe    -     -  {  g£  -     -     - 

MM 

10 

** 

** 

1 

Hamilton  30  in.  Tick 

483 

II3 

* 

** 

2 

Thnrni^ilrp  C1 

###* 

08- 

** 

** 

2 

Wamsutta  C.  Blea.      -     -    gfl  -     -     - 

**#* 

12 

M 

** 

8 

AndrosL.     -    -    -  /g.  g.  g  gl      - 

#** 

073 

** 

** 

1 

T-J                            flrtl  1        1   0    / 

363 

22 

* 

** 

Pir                          /4 

*** 

** 

Cooperage    - 

1 

25 

#**       ** 

106 


PER  CENT  A  GE. 


(10.  Dry  Goods.) 

Book  174,  Page  148.  NEW  YORK,  March  30,  1878. 

Mr.  JAMES  MORGAN,  Milwaukee,  Wis. 

Bought  of  H.  B.  CLAFLIN  &  Co. 

Terms :    Net  6O  Days,  or  \%  discount  in  30  days,  or  2# ) 
discount  in  10  days,  N.  Y.  Funds.    No  Exchange  allowed,  f 


$4641 

53 

PC'S  Gordon  Prints  (Job) 

212  482  38    401  482  483  372  48    48 

44    492  443  482  49*  493  492  42    56 

482  491  282  491  49    483  491  28    48s 

37    332  492  52    333  40    48    491  491 

24    482  482  52    483  49    472  481  482 

49  l  492  483  482  482  432  491  492    - 

***** 

*2601 

54 

PC'S    Do. 

433  48    49    42    221  491  49    482  532 

482  473  483  482  49    44    49    492  482 

492  49    49    48*  473  47    482  491  56 

502  491  411  481  50    271  49    482  483 

213  291  513  463  482  482  282  482  491 

492  452  47    482  402  501  392  482  461 

***** 

«  4765 

61 

PC'S    Do. 

302  492  42    492  32    48    46    482  462 

423  47'  221  33    46    48    492  482  48 

42    42    48   28    481  492  482  49    49 

492  482  282  492  43    491  482  492  48 

382  29    25    263  491  493  491  49    482 

343  483  45    49    491  49a  481  36    48 

292  493  482  311  482  49   481      -    - 

***** 

***** 

.042 

*** 

** 

Cooperage    - 

1 

00 

*•** 

** 

Messrs.  JORDAN,  MARSH  &  Co. 


(11.  Dry  Goods.) 

NEW  YORK,  March  20, 1878. 

Bought  of  A.  T.  STEWART  &  Co. 


Job. 

8 

Cases  Gordon  Fancy 

J.  U. 

$4561        2810 

S.  B.  R. 

4157        29021 

H.  Z. 

3473        2787* 

S.  J.  L. 

4224        2880* 

G.Q. 

2777        2821  l 

J.  B. 

3504        28422 

J.  Z. 

3970        28831 

J.  H. 

4198        28631     -    -    ******  .05 

**** 

** 

Less  5fe     - 

** 

** 

**** 

** 

BILLS.  10? 

(12.  Hosiery.) 

NEW  YORK,  June  28,  1886. 
Messrs.  JOHN  FORD,  SONS  &  Co., 


Claims  for  Damages  or  Errors  must 
be  made  on  receipt  of  Goods. 


Net  SO  Days. 

Note  to  your  own  order 

Payable  at  a  Bank  in  New  York  City. 


Bought  of  JAMES  TALCOTT. 


1789 

35 

Doz.  3458  Mixed  %  Hose      -     -     .80 

28 

25 

"      2032  Fancy  "      "      -     -     -     .80 

##• 

12 

853  Col'd           "     -     -     -  1.00 

** 

12 

"      1691  Fancy         "     -     -    -  1.00 

** 

18 

"      1759      "              «     .    .    .    .75 

** 

## 

20 

«      1713      "              «...  1.00 

## 

16 

"      1716      "              «     -    .    .  1.10 

*# 

** 

6 

"      3438  Fchmx^  "     -    -    -    .90 

•& 

** 

22 

"      Job    Misses        "     -    -     -    .75 

Ml 

** 

$*** 

*# 

Shipped  per  P.R.R.&C.B.  &  Q.R.R. 

Mr.  JOHN  BERWOLD, 

Terms  Cash. 


(13.  Books.) 

CHICAGO,  ILL.,  May  7,  1878. 

Bought  of  HADLEY  BROS. 


12 

18 
24 
36 
18 
12 
6 
6 
6 

Randall's  Arithmetics,  Part  1     -      .60 
"     2     -      .50 
Smith's  Primers  (paper)     -    -     -      .06 
Spellers  .22 
"      2d  Readers  .45 
«      3d       "        .70 
"      4th      "        1.15 
"      5th      "        ....    1.35 
Doz.  Brown's  Copy  Books  -          •    1.80 

7 

20 

#* 

*-K- 
*•» 

Less  33%^ 

#* 

** 

** 

** 

6 
6 
6 
6 

Jones'  Geographies  ft  1  -     -    -    -      .35 
"     .         2-    -     -    -      .63 
3  -    -    -     -    1.10 
4  -    -    -    -    2.00 

2 
* 
* 
fc* 

10 

3 
3 

Less  25  % 

Boxes  Chalk  Crayons     -     -     -     -     .18 
Doz.  Blank  Copy  Books     -    -    -    .50 

* 

*-x- 

** 

t 

** 

$** 

** 

108 


PER  C ENTA  G  E. 


Messrs.  N.  RUTTEE,  SON,  &  Co., 
Terms  60  days. 


(14.  Hardware.) 

PHILADELPHIA,  PA.,  Aug.  13, 1880. 

Bought  of  BIDDLE  HARDWARE  Co. 


24 

Sets  W'd  Wh'l  Bed  Casters  *  1  2  in.     -    .18 

* 

** 

60$   -  - 

* 

«# 

1 

Doz.  Russell's  S.B.  Knives  14  in.  S1540     - 

11 

2.40      2.55     3.15      3.20 

200 

Carriage  Bolts  %   x  1        2^    5%    5% 

Ml 

** 

4.50      4.70      4.90      5.30 

100 

"      Vie  x  534     5%     63^     734 

** 

•sf* 

5.95      6.25      6.50     6.85 

100 

"       H   x  5M    5        63^    6% 

** 

## 

7.15     7.45 

100 

"       "     M  x  734   7%  .... 

** 

** 

7.90                 8.05 

100 

"         "       %    x  8>£             8%    -     - 

** 

## 

6.50     8  00      10.40 

100 

"      Vie  x  2^    4V£    7^    -     - 

** 

** 

10.80      i.1.20 

100 

"       VieX   8         8^    -     -     -     - 

** 

** 

7.25      7.75      9.25 

100 

^    x   2         gjf    4  .     .     - 

#-» 

** 

11.25    11.75    13.25 

100 

"         K    x   6         6^     8  -     -     - 

#* 

*# 

**# 

## 

X 

C.  Machine  Bolts  %  x    8                     8.70 

* 

** 

** 

** 

15.10       16.60 

% 

"     %  x    6           7  -    -    - 

Mt 

** 

99 

Ibs.     "            "Mx  11                   .10^ 

** 

** 

** 

** 

5  Cases                  Packing  and  Cartage    - 

1 

** 

*# 

(15.  "Watches  and  Jewelry.) 

NEW  YORK,  Mar.  7,  1877. 
Mr.  CHARLES  BABCOCK, 

Bought  of  WHEELER,  PARSONS  &  HAYES. 

Terms :  Net  Cash  4  months,  or  lesp  5$  30  days,  with  Exchange  on  New  York. 


H658 
20422 


18  k.  Ancre  17  L.  full  Engrd  &  Enid  S.  W. 

14  k.  Russell  17  L.  flat  C.  B. 

18  k.  Plain  Ring  3%  dwts.  @  !"•  - 

Premium 

14  k.  Guards  with  slides  ^,  ~  @ 
Pr.  Solid  Roman  SI.  Buttons  908    - 


90 
46 


#** 
10 


Gold 


BILLS. 


109 


(16.  Tinware.) 

ROCHESTEB,   N.   Y.,    Oct.    16,   1880. 

Messrs.  MCCARTHY  &  REDFIELD, 

Bought  of  JOHN  H.  HILL. 

Terms  60  days.    If  paid  in  10  days  2  per  cent,  discount. 


2 

Doz.  821  Pieced  Dish  Pans    -     -    8.25 

** 

** 

K 

"    9  in.  Wash  Boilers          -     -  36.00 

** 

3 

"     Pieced  Bread  Pans  3x9x3-     2.00 

* 

3 

"5x9x2-    2.00 

* 

1 

"    85  Pieced  Covered  Pails      - 

2 

50 

3 

"    813    «      Cups      -                     .90 

* 

** 

1 

"    815    "      Dippers      - 

1 

25 

2 

"    825    "            "            ...  .    .    1.75 

* 

#* 

6 

Nests  8021  Flaring  P'ls  &  Dippers  1.14 

* 

#* 

** 

** 

20&12^^     - 

** 

** 

** 

** 

1 

Doz.  Champion  Nutmeg  Graters 

1 

75 

1  Case  .15 

1 

"     Nests  8  4  Fancy  Cov'd  Pails 

6 

00 

15 

1  "    .17 

1 

"    84  Burnished  Tea  Pots  -    r 

6 

75 

17 

*# 

** 

25  &  12%%     - 

* 

** 

* 

** 

1 

"    89  Pudding  Pans  -    -    -    - 

3 

50 

2 

"810      "          "-•;.'.':    4.25 

* 

** 

i^ 

"    8  200  Pressed  Kettles      -    -    5.50 

* 

** 

1 

"    8220      " 

7 

** 

** 

37*^     - 

* 

** 

** 

** 

6 

2  qt.  En'ld  Bel.  Sauce  Pans  -    -      .63 

* 

** 

3  "        "      "        "         "                 .73 

* 

** 

* 

** 

40%     - 

* 

** 

* 

** 

6 

.75    .90 
Enameled  Kettles  Ea.  4—5  qt.    - 

* 

** 

1.10  1.30 

12 

6—  8qt,    - 

** 

** 

80*     - 

11 

*-;;- 

** 

« 

1  Crate 

7 

8—  W.  H.    Tea  Kettles    ...      .95 

45^     - 

* 

*# 

it 

** 

4  Boxes  2.06,  Carting  .38    - 

# 

*» 

#* 

## 

N.Y.C.&H.R.R.9751bs.  Qlty 

110  PERCENTAGE. 

COMMISSION    AND    BROKERAGE. 

279.  Commission  or  Brokerage  is  an  allowance  made  to 
an  agent  for  transacting  business  for  another;   as,  the  sale  or 
purchase  of  property,  the  collection  or  investment  of  money,  etc. 

An  additional  percentage  is  usually  charged  by  commission  merchants  for 
guaranteeing  the  payment  of  sales  made  on  credit. 

280.  The  party  who  transacts  the  business  is  called  a  Com- 
mission  Merchant,  or  Broker;    and  the  one  for  whom  he 
acts  is  called  a  Principal. 

NOTES. — 1.  Commission  Merchants  usually  have  possession  of  the  subject- 
matter  of  the  negotiation,  and  make  sales  and  purchases  in  their  own  name. 

2.  Brokers  do  not  have  possession  of  the  merchandise  bought  or  sold,  and 
generally  make  contracts  in  the  names  of  those  who  employ  them  and  not  in 
their  own.  They  simply  effect  bargains  and  contracts. 

The  name  broker  is  often  erroneously  applied  to  dealers  in  stocks,  bonds, 
etc.,  who  buy  and  sell  on  their  own  account  only. 

281.  A  Consignment  is  a  quantity  of  merchandise  sent  by 
one  party  to  another.     The  party  who  seijdp  it  is  called  the  Con- 
signor ;  and  the  party  to  whom  it  is  sent,  "the  Consignee. 

282.  The  Net  Proceeds  of  a  consignment  is  the  balance  due 
the  consignor  after  all  charges  or  expenses  have  been  deducted. 

The  whole  amount  realized  from  a  sale  is  called  the  gross  proceeds.  The 
commission  is  usually  a  certain  per  csnt.  of  this  amount. 

283.  An  Account  Sales  is  a  detailed  statement  rendered 
by  the  Commission  Merchant  to  the  Consignor,  showing  the  sales 
of  certain  goods,  the  charges  or  expenses  attending  the  same,  and 
the  difference  or  net  proceeds. 

The  charges  embrace  freight,  cartage,  inspection,  advertising,  storage, 
insurance,  commission  and  guarantee,  etc. 

284.  An  Account  Purchase  is  a  detailed  statement  rendered 
by  the  Commission  Merchant  to  his  Principal,  showing  the  cost 
of  certain  goods,  and  the  charges  or  expenses  attending  the  pur- 
chase. 

•    285.  Commission  or  brokerage  is  usually  computed  at  a  cer- 
tain per  cent,  of  the  amount  realized  or  invested,  or  of  the  amount 


COMMISSION    AND    BROKERAGE.  Ill 

involved  in  the  transaction.     In  such  cases  the  general  principles 
of  percentage  are  applied. 

NOTES.— 1.  In  buying  and  selling  stocks,  bonds,  etc.,  the  par  value,  and 
not  the  actual  value,  is  taken  as  the  base. 

2.  The  commission  for  buying:*and  selling  some  kinds  of  merchandise  is 
usually  computed  at  a  certain  price  per  unit  of  weight  or  measurement ;  as, 

grain  per  bushel,  cotton  per  bale,  etc. 

**\^ 

EXAMPLES. 

286.  1.  A  commission  merchant  sold  goods  to  the  amount 
of  $8G4  ;  what  was  his  commission  at  2J-  (J  of  10)  %  ? 

J  2.  A  salesman  sells  goods  at  a  commission  of  2^%  ;  what  must 
be  his  sales,  that  he  may  have  a  yearly  income  of  $5000  ? 

/  3.  What  is  the  brokerage  for  selling  850  fcajies  of^otton  at  the 
rate  of  $25  per  100  bales  ?  *  ^  i 

J  4.  A  lawyer  collected  a  note  of  $2375;  how' much  did  he  pay 
to  the  owner  of  the  note,  his  commission  being  5%  ? 

5.  My  agent  in  Chicago  purchases  for  me  600  barrels  of  flour 
at  $3.75  per  barrel ;  how  much  do  I  owe  him,  his  commission  for 
purchasing  being  2%  ?  4  <.\  f- 

6.  An  officer  collected  $17850,  and  deposited  $17493  in  the 
Treasury,  retaining  the  remainder  as  his  commission.     What  was 
the  rate  per  cent,  of  the  commission  ? 

7.  Sent  to  a  commission  merchant  in  Toledo  $2080.80  to  in- 
vest in  flour,  his  commission  being  2%  on  the  amount  expended; 
how  many  barrels  of  flour  would  be  purchased  at  $4.25  per  barrel  ? 

8.  A  commission  merchant  sells  merchandise  amounting  to 
$3325  ;  how  much  is  paid  \to  the  consignor  of  the  merchandise, 
the  charges  being,  for  transportation  $117.50,  for  advertising  $10, 
for  storage  $15,  for  commission  2-|%  ? 

9.  My  agent  in  Chicago  buys  for  me  1187.76  centals  wheat  at 
$2.123  per  cental.     What  is  his  commission  at  J  per  cent.? 

10.  A  commission  merchant  purchased  for  me  9-^  bushels  of 
clover  seed  at  $8.55  per  bushel.     How  much  should  I  send  to  him 
in  settlement,  if  his  commission  for  purchasing  is  1  per  cent.  ? 

11.  A  broker  buys  8375  pounds  of  leather  at  26  cents  per 
pound.    What  is  his  brokerage  at  |%  and  what  is  the  net  amount 
received  by  the  seller,  the  brokerage  being  paid  by  him  ? 

12.  A  freight  broker  procures  transportation  for  375  tons  of 
merchandise  at  $3.50  per  ton  ;  what  is  his  brokerage  at 


112  PERCENTAGE. 

IS.  A  collector  deposits  $28117,  retaining  3%  on  tlie  whole 
amount  collected.  What  amount  did  he  collect  and  what  v/as  his 
commission  ? 

14.  A  lawyer,  collecting  a  note  at  a  commission  of  6%  thereon, 
received  $6. 25  ;  what  was  the  face  of  the  note  ? 

15.  An  agent  sold  6  mowing-machines  at  $120  each,  and  12  at 
$140  each.     He  paid  for  transportation  $72,  and,  after  deducting 
his  commission,  remitted  $2208  to  the  manufacturer.     What  was 
the  %  of  his  commission  ? 

16.  A  merchant  instructs  his  agent  in  Cincinnati  to  buy  pork 
to  the  amount  of  $5000.     The  charges  on  the  pork  being  $16,  and 
the  agent's  commission  1|%  how  much  must  be  remitted  to  settle 
the  bill? 

17.  What  are  the  net  proceeds  of  the  sale  of  12372  pounds  of 
leather  at  22  cents  per  pound,  the  charges  being  $31,  and  a  com- 
mission of  2-J%  being  paid  for  selling  and  2£%  for  guaranteeing 
payment  ? 

18.  A  real  estate  agent,  who  charged  2J%  for  making  the  sale, 
paid  to  the  owner  of  a  house  and  lot  $42412.50  ;  what  was  the 
value  of  the  property  ? 

19.  A  commission  merchant  sells  240  bbl  of  potatoes  at  $3.75 
per  bbl.,  and  260  bbl.  at  $3.60  per  bbl.     How  much  is  due  the  con- 
signor, the  commission  being  12 \  cents  per  barrel  ? 

20.  John  Smith  is  a  disbursing  agent  of  the  United  States. 
Jan.  1, 1880,  there  is  in  his  hands  $11870.63.     Feb.  1,  he  pays  out 
$3220.34,  on  which  he  is  entitled  to  a  commission  of  \\%.     Mar. 
1,  he  receives  $3750.87.     May  1,  he  pays  out  $3795.01,  on  which 
he  is  entitled  to  a  commission  of  2£%.     Make  a  statement  of  his 
account,  showing  balance  due  the  United  States. 

.  21.  What  are  the  proceeds  in  currency  of  $2611.06  gold,  at 
1.06-|,  commission  for  selling  -fa%  ? 

22.  A,  having  a  claim  against  the  government  of  $10970, 
agreed  to  pay  an  agent  8  per  cent,  of  the  amount  collected.     But 
the  amount  collected  was  22  per  cent,  less  than  the  amount  of  the 
claim.    How  much  was  received  by  A  ? 

23.  B  sends  $2240.70  to  his  agent  in  Cleveland  requesting  him 
to  invest  in  provisions  after  deducting  his  commission  for  pur- 
chasing of  3%  ;  what  was  the  sum  invested  ? 

24.  A  broker  received  $62.50  for  selling  some  bonds,  charging 
\%  brokerage.     What  was  the  par  value  of  the  bonds  ? 


COMMISSION    AND    BROKERAGE. 


113 


25.  A  commission  merchant  sold  300  bales  of  cotton,  averaging 
462  Ib.  to  the  bale,  at  15.70,  his  commission  being  250  per  bale, 
and  the  charges  $161.     He  purchased  for  the  consignor  dry  goods 
amounting  to  $2576.37,  charging  a  commission  of  1|%     How 
much  was  still  due  the  consignor  ? 

26.  A  of  Chicago,  sends  to  B  of  New  Orleans,  8000  bu.  of 
wheat  and  500  Ibis,  of  flour  with  instructions  to  sell  it  and  invest 
the  proceeds  in  sugar.     B  pays  freight  and  cartage  83420 ;  sells 
the  wheat  at  $1.60  per  bushel  and  the  flour  at  $5.25  per  barrel; 
charges  2£%  commission  on  the  flour  and  10  per  bushel  on  the 
wheat :  how  many  pounds  of  sugar  are  purchased  at  8J  cents  per 
pound,  the  commission  for  purchasing  being  3%  ? 

Copy  the  following  accounts,  and  make  the  necessary  exten^ 
sion,  etc. 

(27.    Account  Sales.) 

NEW  YORK,  Oct.  19,  1880. 
Sold  for  account  of  A.  W.  RANDOLPH  &  Co., 

By  DAVID  Dows  &  Co. 


1880. 
Sept. 

M 

Oct. 

12 

18 
30 
14 

18 

100  Bbls.  "  Sunshine  "-     -     -     -    5.75 
125     "       "Pride  of  the  West"  -     6.25 
IfiO    "      "Sunshine"-     -     -     -    6. 
75    "      "  Pride  of  the  West  "  -    6.50 
50    "                                 "          -     6.60 

#•::--* 
•»*# 
### 
**# 

*«•* 

** 
## 

***-::- 

** 

Sspt. 
Oct. 

10 
10 
19 
19 

Charges. 
Transportation  500  Bbls.  @27f-    -     - 
Cartage              400     "       @    5^  -     -     - 
Storage              400    "      @    3^  -     -     - 

*** 
** 
** 
•» 

** 

« 

19 

Commission  and  Guarantee  5%  -     -     - 

##* 

** 

**# 

** 

Net  proceeds      -    -     -     -    - 

**#* 

** 

(28.    Account  Purchase.) 

TOLEDO,  O.,  Mar.  6,  1S77. 
Purchased  by  A.  L.  BACKUS  &  SONS. 

For  account  and  risk  of  L.  A.  &  W.  B.  SHAW. 


9 

227 
928 

Bags  "  Montauk  "     .21 
Bu.  Mammoth  Clover  Seed    -    -    9-- 
"    Clover  Seed    -                              855 

# 

•»* 

931 

"    Timothy  Seed                              I75 

»* 

*** 

** 

Charges. 

OK 

* 

** 

* 

•Jfrvf 

Charffe  vour  ^ 

*** 

** 

114  PERCENTAGE. 

PROFIT    AND    LOSS. 

287.  Profit  and  Loss  treats  of  the  gains  (profits)  and  losses 
which  arise  in  business  transactions. 

'  The  profit  or  loss  is  always  estimated  on  the  cost  price,  or  the  amount 
invested.  "  Discounts  are  reckoned  on  the  market  or  asking  price.  (See 
Art.  274.) 

288.  The  difference  between  the  cost  of  goods  and  the  price 
at  which  they  are  sold  is  a  profit  or  a  loss, — profit  if  the  selling 
price  is  the  greater,  loss  if  the  cost  is  the  greater. 

EXAMPLES. 

289.  1.  A  man  purchased  a  horse  for  $250,  and  sold  it  at  a 
gain  of  16$,    What  was  the  gain  ?     (Gain  =  .1C  x  cost.) 

2.  A  merchant  sold  goods  that  cost  $325  at  an  advance  of  12$; 
what  was  the  selling  price  ?      (Grain  =  .12  x  cost,   and  selling 
price  =  cost  +  gain  ;  or,  selling  price  =  1.12  x  cost.) 

3.  Bought  a  farm  for  $3600,  and  sold  it  at  an  advance  of  25$; 
what  was  the  gain  ? 

NOTE.— If,  as  in  the  above  example,  the  rate  per  cent,  is  an  aliquot  part 
of  100,  it  is  more  convenient  to  use  the  equivalent  fraction  (2712).  Thus, 
25%  =  .25  =  \  ;  gain  —  \  of  cost. 

4.  Cloth  is  bought  at  $6  per  yard,  and  sold  at  a  loss  of  20$. 
What  is  the  selling  price  ?     (Selling  price  =  f  of  cost.) 

5.  Bought  a  house  for  $3475  ;  at  what  price  must  it  be  sold 
to  gain  36$  ? 

6.  Purchased  flour  at  $6.25  per  barrel ;  at  what  price  must  it 
be  sold  to  gain  20$? 

7.  If  I  buy  hats  at  $27  per  dozen,  at  what  price  must  they  be 
sold  apiece  to  gain  33-J-$  ? 

8.  A  factory  which  cost  $8775  was  sold  at  a  gain  of  16%. 
What  was  received  for  it  ? 

9.  If  silk  costs  $1.68  per  yard,  and  is  sold  at  an  advance  of 
12J-$,  what  is  the  profit  per  yard  ? 

10.  A  merchant  purchased  goods  to  the  amount  of  $8735,  and 
sold  them  at  a  loss  of  12$  ;  what  was  his  loss  ? 

11.  Bought  125  barrels  of  flour  for  $600.     If  sold  at  an  advance 
of  15$,  what  was  the  profit  per  barrel  ? 


PROFIT   AND    LOSS.  115 

12.  A  lot  of  dry  goods  was  sold  at  an  advance  of  18$.  If  the 
gain  was  $436.50,  what  was  the  cost  ?  (Gain  =  .18  x cost;  hence, 
gain  -r-  .18  —  cost.) 

18.  A  farm  was  bought  for  $7200,  and  sold  at  a  gain  of  $900  ; 
what  was  the  gain  per  cent.  ?  (Gain  =  gain  %  x  cost ;  hence, 
gain  %  =  gain  -r-  cost.) 

14..  A  man  paid  for  merchandise  1875,  and  sold  it  for  $1015 ; 
what  per  cent,  did  he  gain  ? 

15.  A  man  paid  for  merchandise  $1015,  and  sold  it  for  $875  ; 
what  per  cent,  did  he  lose  ? 

16.  Find  the  rate  %  of  profit  on  goods  bought  for  $324  and  sold 
for  $364.50. 

17.  A  painting  was  sold  for  $2343,  at  a  gain  of  32%  ;  what  was 
the  cost?      [Selling  price  =  1.32  (100%  +  32%)  x  cost ;   hence, 
cost  =  selling  price  ~-  1.32.] 

18.  Find  the  cost  of  goods  sold  at  an  advance  of  12£$,  being 
a  profit  of  $76. 

19.  How  much  was  paid  for  a  farm  sold  for  $9878,  at  12$ 
below  cost  ? 

20.  What  is  the  profit  on  iron  sold  for  $4520,  at  an  advance 
of  13%  on  cost  ? 

21.  What  is  the  selling  price  of  tea  which  cost  32  cents  per 
pound  and  is  sold  at  a  profit  of  37-J-%  ?  <V\ 

22.  Sold  drugs  for  $168,  at  an  advance  of  75$  ;  what  was  the 
profit?  :1/V 

23.  A  merchant  sold  for  $2576  a  lot  of  dry  goods  for  which 
he  paid  $3360.     What  was  the  per  cent,  of  loss? 

24.  A  mixture  is  made  of  1  gallon  of  wine  at  50  cents  a  gallon, 
3  at  90  cents,  4  at  $1.20,  and  12  at  40  cents.     What  per  cent, 
would  be  gained  by  selling  the  mixture  at  $1.60  a  gallon  ? 

25.  If,  by  selling  tea  at  47-|-  cents  per  pound,  1  lose  5%,  at  ^ 
what  price  must  I  sell  it  to  gain  15%  ? 

26.  If,  by  selling  goods  for  $126,  I  lose  16%,  what  per  cent 
would  I  have  lost  or  gained  if  I  had  sold  them  for  $168?  ^  *. 

27.  A  merchant's  price  is  25%  above  cost  price.     If  he  allows  a 
customer  a  discount  of  12%  on  his  bill,  what  per  cent,  profit  does 
he  make  ? 

28.  If   cloth,  when   sold   at   a   loss    of   25%,    brings   $5   per 
yard,    what   would   be   the   gain   or  loss    per   cent,    if    sold   at 
$6.40  per  yard? 


116  PERCENTAGE. 

29.  Goods  that  cost  $168  are  sold  at  an  advance  of  25%;  what 
is  the  selling  price  ? 

30.  What  must  be  the  asking  price  of  goods  costing  $32,  that  I 
may  deduct  20%  from  it,  and  still  gain  25%  on  the  cost  ? 

81.  Sold  a  horse  at  a  gain  of  33^-%,  and  with  the  proceeds  pur- 
chased another  horse,  which  I  sold  for  $120  at  a  loss  of  20%.   What 
was  the  gain  or  loss  ? 

82.  What  must  ribbon  be  sold  per  yard  so  as  to  gain  20%,  if 
22 J  yards  cost  $6. 75? 

88.  Books  are  purchased  at  a  discount  of  30%  from  the  list 
price  (274).  What  is  the  gain  per  cent,  by  selling  at  the  list 
price  ? 

34.  What  per  cent,  is  gained  by  selling  pans  at  21  cents  apiece, 
that  cost  $2.56  per  dozen  less  20  and  12£%  ? 

35.  Plows  are  bought  at  a  Discount  of  50$  from  the  list  price. 
What  per  cent  is  gained  by  selling  at  the  list  price  ? 

86.  A  merchant  purchases  goods  at  a  discount  of  25%  from  the 
list  price.  What  per  cent,  is  gained  by  selling  at  the  list  price. 
What  per  cent,  if  goods  are  purchased  at  a  discount  of  33 \%  ? 
35%  ?  25%  and  5%  ?  20%  and  12J%  ?  15%  and  10%  ? 

37.  A  merchant's  retail  price  for  boots  is  $4.75  per  pair,  by 
which  he  makes  a  profit  of  33J%.  He  sells  to  a  wholesale  customer 
at  a  discount  of  20%  from  the  retail  price.  What  per  cent,  does 
he  gain  or  lose,  and  what  does  he  receive  per  pair  ? 

88.  40  head  of  cattle  weighing  527*70  pounds  are  purchased  in 
Chicago  at  $4  80  per  cwt,  and  are  sold  in  New  York  at  10 \  cents 
per  pound,  to  dress  56  pounds.     What  is  the  gain  per  cent.,  mak- 
ing no  allowance  for  transportation  ?    What  was  the  total  cost  ? 
The  total  selling  price  ? 

NOTE. — The  quantity  bought  or  sold  does  not  affect  the  gain  or  loss  per 
cent. 

89.  A  speculator  sold  two  building  lots  for  $4800  each.     On 
one  he  gained  20%,  and  on  the  other  he  lost  20%.     Did  he  gain  or 
lose,  and  how  much  ? 

40.  If  a  merchant  buys  goods  at  a  certain  price  10  and  5  off, 
and  sells  them  at  the  same  price,  5  off,  what  per  cent,  profit  does 
he  make  ? 

41.  What  must  be  the  asking  price  for  books  that  cost  $1.60, 
in  order  to  abate  20%,  and  still  make  a  profit  of  25%? 


I  NTEREST. 


DEFINITIONS. 

290.  Interest  is  a  sum  charged  for  the  use  of  money,  or  its 
equivalent;  or  more  strictly  speaking,  it  is  the  use  of  money,  or 
the  service  rendered  in  its  use. 

291.  The  Principal  is  the  sum  for  the  use  of  which  interest 
is  charged. 

292.  The  Rate  is  the  per  cent.,  or  number  of  hundredths, 
of  the  principal,  charged  for  its  use  for  a  certain  time,  usually  for 
one  year  (per  annum).     When  no  time  is  mentioned  with  the  rate 
in  the  contract,  a  year  is  understood. 

293.  The  Amount  is  the  sum  of  the  principal  and  interest. 

If  $1000  is  loaned  for  one  year  at  6%  per  annum,  $60  would  be  the 
interest,  $1000  the  principal,  and  $1060  the  amount. 

294.  Simple  Interest  is  interest  on  the  principal  only  for 
the  full  time. 

295.  Compound  Interest  is  interest  not  only  on  the  princi- 
pal, but  on  the  interest  also  after  it  becomes  due. 

If  $1000  is  loaned  Jan.  1,  1881,  for  2  years,  the  amount  due  Jan.  1,  1883, 
at  6%  simple  interest,  would  be  $1000  (Principal)  plus  $120  (Simple  Interest), 
or  $1120.  At  compound  interest  the  amount  due  Jan.  1, 1882,  would  be  $1060 
($1000 +  $60) ;  the  amount  due  Jan.  1,  1883,  would  be  $1060  plus  $63.60  (6% 
of  $1060),  or  $1123.60.  The  simple  interest  for  2  years  would  be  $120;  the 
compound  interest  for  the  same  time,  $123.60.  When  the  word  interest  is 
used  alone,  simple  interest  is  understood. 

296.  Legal  Interest  is  the  interest  according  to  the  rate 
per  cent,  fixed  by  law  for  cases  in  which  the  rate  per  cent,  is  not 
specified.     By  special  agreement  between  parties  in  certain  States, 
interest  may  be  received  at  a  rate  higher  than  the  legal  rate.     In 
most  of  the  States,  this  rate  is  limited.     See  Art.  298. 


118 


INTE  RE  ST. 


297.  Usury  is  the  taking  of  a  higher  rate  of  interest  than 
that  allowed  by  law.     A  person  taking  usury  is  liable  to  certain 
penalties  differing  in  the  several  States. 

298.  The  following  table,  prepared  from  information  received 
from  the  Secretaries  of  the  several  States  and  Territories,  April  1, 
1880,  shows  in  the  first  column  the  legal  rate  of  interest  when  no 
rate  is  specified  in  the  contract,  and  in  the  second  column  the 
maximum  rate  allowed  by  law. 


State  or  Territory. 

Rz 

i*e. 

State  or  Territory. 

Ea 

te. 

8% 

8% 

Mississippi  

6% 

10% 

"Alaska  (Ter  ) 

Missouri              .      ... 

6% 

10% 

Arkansas  

6% 

10% 

10% 

Any 

'•'Arizona  (Ter  ) 

10% 

Any 

Nebraska 

7r/n 

10% 

10% 

Any 

Nevada 

10%; 

dColorado      .  .          ... 

10% 

Any 

New  Hampshire  

6% 

6'£ 

Connecticut    . 

Q7c 

6% 

New  Jersey  

6C<G 

6^1 

Dakota  (Ter  ) 

1% 

12% 

New  Mexico  (Ter  ).  .  . 

Any 

Delaware 

6# 

6% 

"New  York  

6% 

6% 

Florida  

8% 

Any 

North  Carolina  

6% 

8^ 

Georeria  .  . 

1% 

8% 

Ohio  

G# 

8% 

Idaho  (Ter  ) 

10% 

18% 

Oregon  

10% 

12% 

Illinois  

0% 

8% 

Pennsylvania  

6% 

6% 

Indian  (Ter  ) 

6% 

Any' 

6% 

Any 

Indiana              . 

6% 

8% 

South  Carolina  

7% 

7% 

Iowa                     . 

6% 

10% 

6% 

6# 

Kansas 

7& 

12% 

Texas  

8% 

12% 

Kentucky 

6# 

Q% 

Utah  (Ter)  

Louisiana 

5<& 

8<& 

Vermont    

art, 

fi#> 

Maine 

RO/n 

Virginia  

RCL 

Rcf. 

Maryland 

6% 

6% 

Washington  (Ter  )  .  .  . 

10% 

Any 

Massachusetts 

6% 

Any 

"West  Virginia, 

0<& 

8£ 

Michigan 

7^, 

\{\'ff. 

Wisconsin  

7& 

10<#i 

Minnesota  

'  7° 

7% 

10^ 

Wyoming  (Ter.N  

'  /° 
12% 

Any 

(*)  Not  organized. 

(b)  "Pawnbrokers  are  allowed  to  charge  5%  per  month." 

(c)  "On  judgments  recovered  in  the  courts  7%,  but  must  not  be  com- 
pounded in  any  manner." 

(d)  "Most  banks  pay  6%  on  time  deposits  and  charge  from  1  to  2%  per 
month  on  loans." 

(e)  "Advances  payable  on  demand  (call  loans),  of  not  less  than  $5000,  on 
negotiable  collaterals,  are  not  subject  to  the  interest  laws,  but  may  be  made 
for  any  compensation  agreed  upon  in  writing." 


INTEREST.  119 

299.  Interest  for  Parts  of  a  Year.— Although  many  of  the 
States  have  rigid  laws  in  regard  to  the  rate  per  cent,  to  be  charged 
per  annum,  few  of  them  specify  on  what  basis  interest  should  be 
reckoned  for  a  period  of  time  less  than  a  year.  The  following 
methods  are  in  common  use  : 

1.  Finding  the  time  in  months  and  days  (Compound  Subtrac- 
tion, Art.  21O,  1),  and  regarding  the  months  as  twelfths  of  a  year, 
and  the  days  as  thirtieths  of  a  month  or  360ths  of  a  year.     This 
method,  although  implied  by  the  general  interest  laws  *  of  the 
State  of  New  York,  is  not  uniform,  since  it  allows  the  same  interest 
for  February  with  its  2S  days  as  for  March  with  its  31  days.    Its 
results  are  sometimes  greater  and  sometimes  less  than  those  of 
accurate  interest. 

2.  Finding  the  exact  time  in  days  (21O,  2)  and  regarding  the 
days  as  3 60th s  of  a  year.     Since  a  day  is  -g-J-g-  of  a  year,  this 
method  produces  too  great  a  result.     It  is  however  used  by  mer- 
chants, brokers,  and  bankers  generally,  and  by  many  banks  f  in 
discounting  notes.     5%  by  this  method  is  equivalent  to  6^%  accu- 
rate interest. 

3.  Accurate   Interest. — Finding  the  exact   time  in   days 
(21O,  2)  and  regarding  the  days  as  365ths  of  a  year.    This  method 
is  used  by  the  United  States  government,  and  by  some  merchants 
and  banks ;  but,  on  account  of  its  inconvenience  when  interest 
tables  are  not  used,  it  is  not  generally  adopted. 

NOTES.— 1.  By  the  first  method,  the  time  from  July  10  to  Sept.  10,  would 
be  2  months,  and  the  interest  would  be  T2^  or  |  of  the  interest  for  one  year. 
On  $10000  at  6$  for  2  months,  the  interest  would  be  $100  (-J-  of  .06  of 
$10000). 

2.  By  the  second  method,  the  interval  between  the  same  dates  would  be 
62  days,  and  the  interest  would  be  ¥°52ff  of  the  interest  for  one  year.  On  $10000 
at  b%  for  3663ff  of  a  year,  the  interest  would  be  $103.33  (jfo  of  .06  of  $10000). 

*  "  For  the  purpose  of  calculating  interest,  a  month  shall  be  considered  the  twelfth  part 
of  a  year,  and  as  consisting  of  thirty  days  ;  and  interest  for  any  number  of  days  less  than  a 
month  shall  he  estimated  by  the  proportion  which  such  number  of  days  shall  bear  to  thirty." 
(R.  8.,  page  1165.) 

t  According  to  the  banking  laws  of  the  State  of  New  York,  banks  are  authorized  in 
discounting  notes  to  charge  interest,  in  advance  for  the  exact  number  of  days  which  the 
note  has  to  run  (Ch.  XVIII,  Title  2,  §  300). 

This  law  appears  to  conflict  with  the  law  quoted  above  which  implies  that  the  time 
shall  be  found  in  months  and  days.  It  does  not  state  whether  tbe  days  shall  be  regarded  as 
360ths  or  365ths  of  a  year. 


120  INTEREST. 

3.  By  the  third  method,  the  interval  between  the  same  dates  would  be 
62  days  as  in  the  second  method,  and  the  interest  would  be  ^  of  the  interest 
for  one  year.    On  $10000  at  Q%   for  -/fa  of  a  year,  the  interest  would  be 
$101.92  (gVir  of  .06  of  $10000). 

4.  The  difference  between  ordinary  interest  and  accurate  interest  for  the 
same  number  of  days  is  ^  of  the  former,  or  ^  of  the  latter  (317).     Thus  in 
the  above  example,  the  difference  between  the  results,  $1.41  ($103. 33-101.92), 
is  ^  of  $103.33,  or  ^  of  $101.92. 

5.  Unless  the  words  "  Accurate  Interest "  are  used,  all  computations  in 
this  book  are  made  on  the  basis  of  360  days  to  the  year. 

300.  Interest  is  an  application  of  percentage,  the  element 
of  time  being  introduced.     Therefore  the  four  elements  or  parts 
in  interest  are  the  Principal  (the  Base),  the  Rate,  the  Interest 
(the  Percentage),  and  the  Time ;  any  three  of  which  being  given, 
the  other  may  be  found. 

301.  To  find  the  interest  for  any  number  of  years  and 
months. 

Ex.     What  is  the  interest  and  amount  of  $324,  for  2  yr.  3  mo., 
at  S%? 

OPERATIONS. 

$324     Principal.  Or  8324 

.18 

IntereBtforlyr.  2592 

324 


58.32 
324. 

Interest  for  2*  yr.  $382. 32 

Principal. 

Amount  for  2£  yr. 

ANALYSIS.— At  8%,  the  interest  of  $324  for  1  year  is  .08  of  $324  (the 
Principal),  or  $25.92.  If  the  interest  of  $324  for  1  year  at  8%  is  $25.92,  for 
2  yr.  3  mo.  (2£  yr.\  it  is  2£  times  $25.92,  or  $58.32.  The  amount  is  $324  plus 
$58.32,  or  $382.32. 

3O2.  RULE. — To  find  the,  interest,  multiply  the  principal 
by  the  rate  per  cent,  expressed  decimally,  and  that  product 
~by  the  number  of  years,  and  the  months  as  a  fraction  of  a 
year. 

To  find  the  amount,  add  the  principal  to  the  interest. 


INTEREST.  121 

NOTES.— 1.  When  the  rate  per  month  is  given,  apply  the  same  rule,  i.e., 
multiply  the  principal  by  the  rate  per  month  expressed  decimally,  and  that 
product  by  the  number  of  months. 

2.  Instead  of  multiplying  by  the  rate  and  time  separately,  the  process  may 
be  shortened  by  multiplying  the  principal  by  the  product  of  the  rate  and 
time.  In  the  above  example,  multiply  $324  by  .18  (2£  x  .08). 

EXAMPLES. 

303.  Find  the  interest  of 

1.  $875  for  2  yr.  at  1%.  6.  $816.40  for  5  yr.  3  mo.,  at  5$. 

2.  $642.50  for  3  yr.  at  §%.  7.  $1275  for  7  yr.  at  Gfc> 

3.  $1010.10  for  6  yr.  6  mo.,  at  8$.  8.  $2789.40  for  3  yr.  2  mo.,  a 

4.  $3010.75  for  3  yr.  4  mo.,  at  1%  9.  $456.75  for  4  yr.  8  mo.,  at 

5.  $3745. 80  for  4  yr.  1  mo.,  at  6$.  .#?.  $10180  for  3  yr.  4  wo. ,  at 

NOTE. — In  the  folio  wing  examples  find  the  time  by  Compound  Subtraction. 

11.  What  is  the  interest  of  $6488  from  May  3,  1879,  to  Sept. 
3,  1881,  at  7^? 

12.  What  is  the  amount  of  $396.60  from  Aug.  16,  1880,  to 
Dec.  16,  1882,  at  S%? 

13.  Find  the  interest  of  $864.30  from  Jan.  1,  1881,  to  June  1, 
1883,  at  4$. 

14.  Compute  the  interest  of  $250.75  from  Nov.  20,  1882,  to 
July  20,  1884,  at  ty%. 

15.  Loaned  on  interest,  New  York,  Dec.  16,  1880,  $1739.75 
(no  rate  specified);  what  amount  should  I  receive,  June  16,  1881  ? 

16.  In  settling  with  a  merchant  Oct.  3,  1882,  I  gave  my  note 
for  $254.60,  at  7^;  what  must  be  paid  Aug.  3,  1883  ? 

304.  To  find  the  ordinary  interest  (360  days  to  the 
year)  for  any  rate  and  time. 

305.  60-day  Method  at  6%. — 6%  for  12  months  or  1  year, 
is  equivalent  to  \%  for  2  months  (60  days),  or  -J-  of  one  year.     \% 
of  any  amount  is  readily  ascertained  by  placing  the  point  two 
places  to  the  left.     Hence  the  interest  of  any  sum  at  6%  per  annum 
for  2  months,  or  60  days,  may  be  found  by  placing  the  point  two 
places  to  the  left. 

NOTE. — It  will  be  found  advantageous  to  use  a  perpendicular  line  as  a 
separatrix  in  solving  examples  by  this  method.  All  necessity  for  pointing 
off  will  then  be  dispensed  with,  and  confusion  prevented. 


122  INTEREST. 

Ex.    What  is  the  interest  of  $1236  for  80  da.,  at  6%  ? 


OPERATION. 


$12 


$16 


36  —  int.  for  60  da. 
12  = 

48  = 


"  20  da. 
"  80  da. 


ANALYSIS.— The  interest  of  $1236  at 
§%  for  60  da.  is  found  to  be  $12.36, by  the 
process  already  explained.  If  the  interest 
for  60  da.  is  $12.36,  for  20  da.  (\  of  60),  it 
will  be  i  of  $12.36,  or  $412.  Hence  for 


80  da.,  it  will  be  $12.36  plus  $4.12,  or  $16.48. 


Ex.    What  is  the  interest  of  $864  for  1  yr.  10  mo.  15  da., 


$8 
"95" 

Q 


$97 


OPERATION. 

64  =  int.  for  60  da. 

n 

04  =  int.  for  22  mo. 
16  =    "      "  15  da. 

20  =  required  int. 


ANALYSIS.— The  interest  of  $864  at 
Q%  for  2  mo.  is  $8.64.  For  1  yr.  10  mo. 
(22  mo.),  it  will  be  11  times  $8.64,  or 
$95.04.  If  the  interest  for  60  da.  is  $8.64, 
for  15  da.  (£  of  60),  it  will  be  £  of  $8.64/ 
or  $2.16.  Hence  the  interest  for  the  given 
time  will  be  $95.04  plus  $2.16,  or  $97.20. 


at 


Ex.     What  is  the  interest  of  $1732.80  for  2  yr.  9  mo.  23  da. 


OPERATION. 


$17     32.80     =  int.  for  2  mo.  or  60  da. 


8 

6640 

103 

9680 

173 

280 

5 

776 

866 

6)292 

554 

48 

759 

$341 

313 

int.  for  20  da. 

((          ((         Q      (( 

"     "  given  time  at  §%. 

"     "       "  1%. 


ANALYSIS. — The  interest  for  2  mo.,  forming  the  basis,  is  $17.328.  Mul- 
tiply this  by  16!,  to  fin(i  tlie  interest  for  33  mo.  (2  yr.  9  mo.}.  As  23  is  not  an 
aliquot  part  of  60,  take  20,  which  is  £  of  60,  and  3,  which  is  ^  of  60.  Divide 
the  basis,  which  is  the  interest  for  60  da.,  by  3,  to  find  the  interest  for  20  da. 
($5.776) ;  and  the  same  sum  by  20,  to  find  the  interest  for  3  da.  ($0.866).  By 
adding  these  various  sums,  we  have  the  interest  for  the  given  time  at  Qfo 
($292.554).  To  this  result  add  £  of  itself,  which  is  the  interest  for  the  given 
time  at  1  % ,  and  the  required  interest  is  obtained  ($341.31). 


INTEREST.  123 

306.  Aliquot  Parts   of  60.— 1  =  ^ ;    %=£>',   3  =  ^ ; 
4  =  A;    5  =  A;    6  =  ^;   10  =  i;    12  =  i  ;   15  =  };  20  =  i; 
30  =  f 

NOTES. — 1.  To  divide  by  10,  place  the  figures  of  the  basis  one  place  to 
the  right. 

2.  To  divide  by  20,  30,  or  60,  divide  by  the  first  figure  and  write  the 
quotient  figures  one  place  to  the  right. 

307.  If  the  number  of  days  given  is  other  than  any  of  the 
above,  which  are  aliquot  parts  of  60,  it  will  need  to  be  so  separated 
that  the  component  parts  will  be  aliquot  parts  of  60. 

Numbers  not  aliquot  parts  of  60,  with  best  divisions :  7=6  +  1  ;  8  =  6  +  2; 
9  =  6  +  3;  11  =  6  +  5,  or  10  +  1;  13  =  10  +  3;  14=12  +  2;  16=10  +  6;  17 
=  12  +  5,  or  15  +  2 ;  18  =  12  +  6.  (The  interest  for  18  days  may  be  found  by 
multiplying  the  basis  by  3,  and  placing  the  figures  of  the  product  one  place  to 
the  right);  19  =  15  +  4,  or  10  +  6  +  3;  21  =  15  +  6;  22  =  20  +  2  (2  =  TV  of  20); 
23  =  20  +  3  ;  24  =  12  + 12  (Or  multiply  by  4  and  place  the  figures  of  the  product 
one  place  to  the  right) ;  25  =  20  +  5  (5  =  \  of  20) ;  26  =  20  +  6  ;  27  =  12  + 15  ; 
28  =  12  +  12  +  4  (4  =  i  of  12),  or  20  +  6  +  2  ;  29  =  12  +  12  +  5,  or  20  +  6  +  3. 

308.  RULE. — Draw  a  perpendicular  line  two  places  to  the 
left  of  the  decimal  point;  the  result  will  be  the  interest  at  6% 
for  2  months,  or  60  days,  the  dollars  being  on  the  left,  and 
the  cents  on  the  right  of  this  line.     Multiply  this  result  by 
one-half  the  total  number  of  months.     To  this  product,  add 
that  proportion  of  the  interest  for  60  days,  which  the  given 
number  of  days  is  of  60. 

309.  The  interest  for  any  other  rate  may  be  found  from  the 
interest  at  Q%  as  follows :  At  \%,  divide  by  6  ;  at  \\%,  divide 
by  4  ;  at  2%,  divide  by  3  ;  at.  3%,  divide  by  2  ;  at  4%,  subtract  J  ; 
at  4-1%  subtract  J ;  at  5#,  subtract  | ;  at  7$,  add  £ ;  at  8#,  add 
J ;  at  9$,  add  £ ;  at  10$,   divide  by  6,  and  multiply  by  10  by 
placing  the  point  to  the  right  one  place ;  at  12$,  multiply  by  2. 
At  any  per  cent.,  divide  by  6  and  multiply  by  the  rate. 

310.  6%  Method.— At  6^,  the  interest  for  one  year  is  .06 
of  the  principal.     For  one  month,  ^  of  a  year,  it  will  be  -fa  of 
.06,  or  .OOJ  (.005).     For  one  day,  ^  of  a  month,  it  will  be  ^  of 
.005,  or.000£. 


124  INTEREST. 

Ex.     What  is  the  interest  of  $864,  at  $%,  for  2  yr.  7  mo.  20  da.  ? 

OPERATION. 

2  x  .06      =  .12 
7  x  .OOJ    =  .035 

20  X  .OOOJ-  =  .003£  ANALYSIS.— If  the  interest  for  1  yr.  is  .06  of 

the  principal,  for  2  yr.  it  will  be  twice  .06,  or  .12. 
If  the  interest  for  1  mo.  is  .00^  of  the  principal, 
for  7  mo.  it  will  be  7  times  .00  J,  or  .035.     If  the 
-j  Koj,  interest  for  1  day  is  .000|  of  the  principal,  for 

20  da.  it  will  be  20  times  .000£,  or  .003  J.     Hence 
288  the  interest  for  the  given  time  will  be  .158£  of  the 

6912  principal  ($864),  or  $136.80. 

4320 
_864_ 
$136.800 

311.  RULE. — Multiply  the  given  principal  by  the  decimal 
obtained  by  taking  for  every  year  six  hundredths,  one-half 
as  many  hundredths  as  there  are  months,  and  one- sixth  as 
many  thousandths  as  there  are  days.     The  product  will  be 
the  interest  at  6%. 

NOTES. — 1.  In  using  this  method,  to  multiply  by  f ,  write  £  twice  ;  to  mul- 
tiply by  f ,  take  £  and  i. 

2.  The  interest  at  any  other  per  cent,  may  be  found  as  in  Art.  3O9. 

3.  The  decimal  obtained  by  the  above  rule,  if  regarded  as  cents  and  mills, 
expresses  the  interest  of  $1  for  the  given  time  at  6%.     The  interest  of  $1  at 
6%  for  1  year  is  $.06 ;  for  1  month,  $.00^,  or  $.005  ;  for  1  day,  $.000^. 

312.  6%  Method  for  Days.— This  is  a  modification  of  the 
preceding  method,  and  may  be  applied  to  any  example  if  the  time 
is  reduced  to  days. 

Ex.     What  is  the  interest  of  $1735  for  173  days  at  §%  ? 

OPERATION. 

$1735 

173  ANALYSIS.— The  interest  of  $1735  for  173  days  is  equiv- 

alent  to  the  interest  of  173  times  $1735,  or   $300155  for 

1  day.     Since  the  interest  of  $1  for  1  day  is  $  of  a  mill,  or 

12145  .000£  of  the  principal,  the  interest  of  $300155  for  1  day  is  as 

1735  many  mills  as  6  is  contained  times  in  300155,  or  50025  mills, 

6  )  300155 


or 


$50.025  + 


OF  THE 

UNIVERSITY 

OF 


INTEREST.  125 

313.  EULE.  —  Multiply  the  principal  by  the  number  of 
dctfijs,  divide  the  product  by  6,  and  place  the  point  3  places 
to  the  left.  TJie  result  will  be  the  interest  at  6%. 

NOTES.  —  1.  The  interest  at  any  other  per  cent,  may  be  found  as  in 
Art.  3O9.  To  find  the  interest  at  3  %  ,  divide  by  12  instead  of  6  ;  at  4  %  ,  by  9  ; 
at  9/0,  by  4. 

2.  If  the  principal  is  a  multiple  of  the  divisor  (6  in  the  above  example), 
time  can  be  saved  by  performing  the  division  first.  Thus,  to  find  the  interest 
of  $1200  for  113  days,  divide  1200  by  6,  and  multiply  the  quotient  200  by  113, 
producing  22600.  By  pointing  off  three  places,  the  required  interest  is  $22.60, 

EXAMPLES. 

314.  What  is  the  interest  of 
-1.  $375.60  for  8  mo.  20  da.,  at  6%  ? 
2.  $1727  for  7  mo.  15  da.,  at  Q%  ? 
8.  $449.38  for  1  yr.  4  mo.  12  da.,  at  6%  ?    At 
4.  $285  for  1  yr.  5  mo.  10  da.,  at  §%  ?    At  6%  ? 
o.  $432.65  for  2  yr.  2  mo.  6  da.,  at  §%  ?     At  8%  ? 

6.  $1235  for  2  yr.  5  mo.  5  da.9  at  6%  ?    At  4%  ? 

7.  $445.25  for  5  mo.  4  da.,  at  6%  ?    At 
$1000  for  93  days,  at  $%  ?    At  1    ? 
$2416.60  for  72  days,  at  6^  ?     At 
$3210  for  62  days,  at  Q%  ?    At  8%  ? 
$735  for  75  days,  at  6%  ?    At  5%  ? 
$812.45  for  121  days,  at  6%  ?    At  4%  ? 

tf&  $2440.50  for  97  days,  at  6%  ?    At  7^  ? 

14.  $3125  for  38  days,  at  6^  ?    At  7^  ?       / 

15.  $247.50  for  69  days,  at  6%  ?    At  §%  ? 

10.  $512.45  for  5  mo.  11  da.,  at  6^  ?    At  1%  ? 

17.  $1478  for  1  yr.  2  wo.  13  da.,  at  6^  ?    At 

1£.  $2810.60  for  9  mo.  24"  <fo,  at  6^  ?    At  5^  ? 

IP.  $944.50  for  1  yr.  10  wo.  22  da.,  at  6$  ?    At 

£0.  $575  for  2  #r.  8  mo.  16  J«.,  at  6^  ?    At  9%  ? 

21.  $1112  for  3  mo.  14  da.,  at  6%  ?    At  Q%  ? 

0&  $5285  for  1  yr.  6  mo.  21  da.,  at  6^  ?     At  3%  ? 

#&  $7218  for  11  wo.  18  do.,  at  6^  ?    At 

&f.  $416.75  for  8  mo.  17  do.,  at  6^  ?    At 

#5.  $1235  for  2  yr.  1  mo.  19  da.,  at  6%  ?    At 

26.  $575.60  for  1  yr.  4  mo.  23  da.,  at  6%  ?    At 

#7.  $2214  for  4  mo.  25  da.,  at  6%  ?    At 


126  INTEREST. 

28.  $6315  for  5  mo.  29  da.,  at  6%  ?    At  9$  ? 

£0.  $4312  for  4  mo.  26  da.,  at  6%  ?    At  4J$  ? 

30.  $384.30  for  2  mo.  28  rf«.,  at  6$  ?    At  3$  ? 

#./.  $1296  for  1  yr.  11  wo.  27  da.,  at  6$  ?    At 

3&  $4375  for  2  yr.  8  wo.  24  <fo.,  at  6$  ?    At 


NOTE.  —  Find  the  time  in  the  following  examples  both  in  months  and 
days,  and  in  exact  days  (21O). 

33.  $1234  from  May  10  to  Dec.  4,  at  5%  ?    At  4|$  ? 

34.  $444.40  from  Jan.  13  to  Nov.  2,  at  4%  ?    At  5J$  ? 

55.  $575.20  from  June  5,  1882,  to  Feb.  4,  1883,  at  7$? 
At  5$? 

36.  $2375  from  July  17,   1884,  to   Nov.    27,   1885,  at  6$? 
At  3£$? 

37.  $3212  from   Aug.    24,    1881,   to   Jan.  20,  1884,  at  4$  ? 
At  4£$? 

S3.  $475.80  from  May  12,  1882,  to  Feb.  1,  1884,  at  7^? 
At  10$  ? 

39.  Find  the  interest  of  $180  for  253  days,  at  6$.     At  8%. 

NOTE.  —  In  many  examples,  labor  can  be  saved  by  having  the  time  and 
principal  exchange  places.  In  the  above  example,  the  interest  of  $180  for 
258  days  is  the  same  as  $253  for  180  days  ($2.53  x  3). 

40.  Find  the  interest  of  $600  for  173  days  at  9$.     At  4$. 

41.  Find  the  interest  of  $3000  for  111  days  at  12$.     At  3$. 

42.  Find  the  interest  of  $1800  from  Jan.  17  to  Oct.  2,  at  6$. 
At  4$#. 

48.  Find  the  interest  of  $540  from  May  11  to  Dec.  18,  at  5$. 
At  ±\%. 

44.  If  $9200  is  loaned  Sept.  18,  1882,  at  6$,  what  is  due 
May  9,  1885?     (Time  by  C.  S.) 

45.  What  is  a  banker's  gain  in  1  year  on  $10000  deposited  at 
6$,  and  loaned  11  times  at  \\%  a  month  ? 

46.  A  note  for  $1421,  with  interest  after  4  months,  at  7$,  was 
given   Dec.  1,  1881,  and  paid  Aug.  12,  1883.     What  was  the 
amount  due?     (C.  S.) 

47.  Nov.  6,  1881,  I  bought  a  lot  of  grain  for  $753.20  ;  Dec.  16, 
I  sold  a  part  of  it  for  $375.60;  and,  Dec.  31,  I  sold  the  remainder 
for  8411.40.     Money  being  worth  6$,  how  much  did  I  gain  by  the 
transaction  ? 


ACCURATE    INTEREST.  127 


ACCURATE     INTEREST. 

315.  To  find  the  accurate  interest  (365  days  to  the 
year)  for  any  rate  and  time.    See  Art.  299. 

Ex.    What  is  the  accurate  interest  of  $865,    at  4^,  from 
June  21  to  Dec.  13  ? 

OPEKATION. 

$865     Principal.  ANALYSis.-From  June  21  to  Dec.  13, 

there  are  175  days.     The  interest  of  $865 
for  1  yr.,  at  4#,  is  $34.60.     For  175  days, 


34.60      Interest  for  1  yr.  /175  x  34.60\ 

1  75  itt  of  1  yr.,  it  is  HI  of  $34.60  ^  -  ^  -  j  , 

365  )605(MJO(  16.59  or  $16.59. 

316.  RULE.  —  Multiply  the  principal  ~by  the  rate  per  cent. 
expressed  decimally.  The  result  will  be  the  interest  for 
1  year. 

Multiply  the  interest  for  1  year  by  the  number  of  days, 
and  divide  the  product  by  365. 

NOTES.—  1.  When  the  number  of  days  is  a  multiple  of  5,  multiply  by  £ 
the  number  of  days,  and  divide  the  product  by  73.  In  the  above  example, 
$865  x  .04  x  35  -s-  73  =  $16.59. 

2.  To  find  the  interest  at  any  per  cent.,  multiply  by  twice  the  rate  as  an 
integer,   by  the  number  of  days,  divide  the  product  by  73,  and  point  off 
3  places.     In  the  above  example,  $865  x  8  x  175  -r-  73000  =  $16.59. 

3.  To  find  the  interest  at  5%,  multiply  the  principal  by  the  number  of 
days,  divide  the  product  by  73,  and  point  off  2  places.     From  this  result  to 
find  the  interest  at  6%,  add  £  ;  ty%,  subtract  TV  ;  ±%,  subtract  £. 


317.  Accurate  Interest  from  Ordinary  Interest.  —  The 
difference  between  ordinary  interest  and  accurate  interest  for 
1  day  equals  the  difference  between  -^  and  -g-J-y  of  a  year's 
interest. 

JL       JL  -  365  —  360  _  5  _5_        J.  1_ 

360  ~~  365  ~~  365  x  360  ~~  365  x  360  ~"  365        360  ~~  73  ° 
J^     _  5_  5^  1_       _!_     .  _1_ 

360*    365  x  360  ~~  360  °    365  ~~  72  °    365* 

The  difference  between  the  two  methods  is  ^  of  ordinary  interest,  or  ^2 
of  accurate  interest  (299,  Note  4).  Therefore,  from  ordinary  interest  to  find 
accurate  interest  subtract  . 


128         .  INTEREST. 

In  reckoning  accurate  interest,  on  account  of  the  many  short  methods  of 
ordinary  interest,  many  accountants  prefer  to  calculate  ordinary  interest  first, 
and  then  make  the  necessary  deduction. 

Since  YV  is  about  li%,  the  following  approximate  method  may  be  used 
in  reducing  ordinary  interest  to  accurate  interest  :  From  the  ordinary  interest 
subtract  1%  and  \%  of  itself. 

Ex.     Reduce  $32.70  ordinary  interest  to  accurate  interest. 

OPEBAT10N. 

32.70  NOTE.—  The  exact  result  should  be  $32.252.      The 

.327     \%          results  by  this  method  are  too  great  by  1  cent  for  each  $27 

oToTo"  interest  ;  $.036  for  each  $100  interest  ;  $.36  for  each  $1000 

interest.     Where  greater  accuracy  is  required,  the  neces- 

3/0          Bary  correction  can  be  made. 


32.264 

EXAM  PLES. 
318.  What  is  the  accurate  interest  of 

1.  $435.32,  at  6#,  for  25  days  ?  5.  $292,  at  3ffl,  for  140  days  ? 

2.  $6030,  at  5$,  for  141  days?   6.  $438,  at  6#,  for  210  days? 

3.  $780,  at  6#,  for  90  days?        7.  $350,  at  4$,  for  150  days? 

4.  $437.80,  at  7$,  for  63  days  ?  8.  $500,  at  4|#>  for  100  days  ? 
9.  $3110.45,  at  5J#,  for  90  days  ? 

m  $373.70,  at  1%,  from  June  4  to  Dec.  28  ? 

11.  $500,  at  6#,  from  July  24,  to  Sept.  16  ? 

7£.  $365,  at  6%,  from  June  30  to  Dec.  21  ? 

18.  $1080,  at  5#,  from  May  9,  1878,  to  Jan.  30,  1879  ? 

14.  $1728,  at  1%,  from  Jan.  6,  1878,  to  Jan.  21,  1880  ? 

15.  Required  the  exact  interest  on  three  U.  S.  bonds  of  $5000 
each,  at  3J$,  from  July  1  to  Aug.  11. 

16.  What  is  the  interest  on  three  U.  S.  bonds  of  $1000  each,  at 
4J#,  from  Sept.  1  to  Nov.  15  ? 

17.  What  is  the  interest  on  a  $5000  U.  S.  bond,  at  4$,  from 
Oct.  1  to  Dec.  16  ? 

18.  What  is  the  interest  on  a  U.  S.  bond  of  $1000,  bearing 
3J$  interest,  from  May  1  to  July  19  ? 

19.  What  is  the  interest  on  a  $500  IT.  S.  bond,  at  4$,  from 
Apr.  1  to  May  10  ? 

W.  What  is  the  interest  on  a  $5000  U.  S.  bond  from  Nov.  1, 
1881,  to  Jan.  3,  1882,  at  3J^? 

21.  What  is  the  difference  between  ordinary  and  accurate 
interest  of  $10000  for  219  days  at  6%? 


PROBLEMS.  129 


PROBLEMS     IN     INTEREST. 

319.  To  find  the  rate,  the  principal,  interest  or  amount, 
and  time,  being  given. 

Ex.    At  what  rate  will  $720  in  1  yr.  4  mo.  10  da.,  produce 
$44.10  interest? 

OPERATION.  ANALYSIS.  —  The    interest    on    a 


$7 


57 


20  given  principal  for  a  given  time  is  in 

o  proportion  to  the  rate  per  cent.     At  one 

per  cent.,  $720  will  in  1  yr.  4  mo.  10  da., 


produce    $9.80  interest.      To    produce 


20  $44.10  interest,  the  required  rate  must 

^  be  as  many  times  1  %  ,  as  $9.80  are  con- 

tained times  in  $44.10,  or  4|  times. 
80  )  $44.10  (  4|-  Ans.        Hence  the  answer  is  41 


6)58 

'   $9 

32O.  EULE. — Divide  the  given  interest  ~by  the  interest  of 
the  given  principal,  for  the  given  time,  at  1%. 

NOTE. — When  the  amount  is  given,  find  the  interest  by  subtracting  the 
principal  from  the  amount. 

EXAM  PLES. 

321.  At  what  rate  will 

1.  $864  in  8  mo.  10  da.  produce  $42  interest  ? 

2.  $1000  in  9  mo.  9  da.  produce  $54.25  interest  ? 

3.  $852  in  1  yr.  7  mo.  16  da.  amount  to  $935.21  ? 

4.  $1926  in  2  yr.  8  mo.  24  da.  produce  $263.22  interest  ? 

5.  $375.60  in  1  yr.  10  mo.  22  da.  amount  to  $425.41  ? 

6.  $1872  in  7  mo.  17  da.  produce  $41.31  interest  ? 

7.  $435.60  in  1  yr.  2  mo.  18  da.  amount  to  $478  ? 

8.  $1338.72  in  6  mo.  27  da.  produce  $34.64  interest? 

9.  $1728  in  8  mo.  21  da.  amount  to  $1778.11  ? 

10.  $3456  in  5  mo.  8  da.  produce  $91.01  interest  ? 

11.  $5280  in  11  mo.  11  da.  amount  to  $5720.12  ? 

12.  $1234  in  8  mo.  22  tfa.  produce  $80.83  interest  ? 
^.  $6975  in  3  mo.  28  da.  amount  to  $7215.06  ? 

14.  $525  in  1  yr.  11  mo.  18  f/or.  produce  $309.75  interest? 

15.  $500  in  3  yr.  11  mo.  12  da.  amount  to  $658  ? 

16.  $4680  in  2  yr.  6  mo.  11  rfa.  produce  $710.58  interest  ? 

17.  $614.45  in  162  days  amount  to  $633.805? 


130  INTEREST. 

322.  To  find  the  time,  the  principal,  interest  or  amount, 
and  rate,  being  given. 

Ex.     In  what  time  will  $426,  at  6$,  produce  $59.427  interest  ? 

OPERATIONS. 

$426  Or   $426 

.06  .06 


$25. 56)  $59. 427  (yr.  2.325     $25.56  )  $59.427  (  2  yr. 
51  12      _J.2  51  12 

8307  mo.  3.900  8.307 

7  668       30  12 

6390  da.  27.000  $25.56  )  99.684  (  3  mo. 
5112  76.68 

12780  23.004 

12780  30 

0  $25. 56)  690. 120  (  27  da. 

ANALYSIS. — The  interest  on  a  given  principal  at  a  given  rate  %,  is  in 
proportion  to  the  time.  In  one  year,  $426,  at  6%,  will  produce  $25.56 
interest.  To  produce  $59.427  interest,  it  will  require  as  many  years  as  $25.56 
is  contained  times  in  $59.427,  or  2.325  yr.  2.325  yr.  equal  2  yr.  3  mo.  27  da. 

(201). 

323.  RULE. — Divide  the  given  interest  by  the  interest  of 
the  given  principal,  at  the  given  rate,  for  1  year. 

The  integral  part  of  the  quotient  will  be  years.  Reduce 
the  decimal,  if  any,  to  months  and  days  (2O1). 

EXAM  PLES. 

324:.  In  what  time  will 

1.  $3000,  at  7$,  produce  $108.50  interest? 

2.  $1728,  at  6%,  amount  to  $1872  ? 

8.  $3932,  at  1%,  produce  $597.88  interest? 

4.  $735,  at  5%,  amount  to  $742.66  ? 

5.  $1222.25,  at  6$,  produce  $39.52  interest? 

6.  $375.60,  at  7#,  amount  to  $425.41  ? 

7.  $1461.75,  at  6#,  produce  $420.25  interest? 

8.  $1200,  at  3}%,  amount  to  $1413  ? 

9.  $4500,  at  5%,  produce  $181.25  interest  ? 
10.  $276.50,  at  10$,  amount  to  $303.46  ? 


PROBLEMS.  131 


11.  $1020,  at  6%,  produce  $89.25  interest? 

12.  $6495,  at  1%,  amount  to  $7161.81  ? 

13.  $100,  at  Q%,  produce  $100  interest  ? 

14.  $125,  at  1%,  amount  to  $375  ? 


To  find  the  principal,  the  interest,  time,  and  rate, 
being  given. 

Ex.     What  principal  will  produce  $152.64  interest,  in  1  yr. 
5  mo.  20  da.,  at  6^? 

OPERATION. 

$.088J)  $152.64(1728. 


>     *  ANALYSIS.  —  The  interest  on  any  principal 

5  is  as  many  times  greater  than  the  interest  of 

1929  $1,  as  that  principal  is  greater  than  $1.     One 

1855  dollar,  in  1  yr.  5  mo.  20  da.,  at  Q%  (31O),  will 

—  —  —  produce  $.088^  interest.  To  produce  $152.64,  the 

principal  must  be  as  many  times  $1  as  $.088£-  is 

530  contained  times  in  $152.64,  or  $1728. 

2120 

2120 


326.  RULE.  —  Divide  the  given  interest  by  the  interest  of 
for  the  given  time,  at  the  given  rate. 

EXAMPLES. 

327.  What  principal  will  produce 

1.  $1235  interest,  in  1  yr.  8  mo.  12  da.,  at  6%  ? 

2.  $49.81,  in  9  mo.  24  da.,  at  1%  ? 

8.  $186.75,  in  1  yr.  4  mo.  20  da.,  at 

4.  $244.44,  in  7  mo.  18  da.,  at  5%? 

5.  $375.60,  in  2  yr.  4  wo.  6  <?«.,  at 
0.  $54.25,  in  3  mo.  3  efo.,  at  1%  ? 
7.  $387.40,  in  2  yr.  8  wo.,  at 

&  $456,  in  93  da.,  at  6^  ? 

9.  $375,  in  63  da.,  at  7%? 

10.  $1000,  in  1  yr.  18  <fe.,  at 

11.  $538.80,  in  10  mo.  24  da.,  at 
1£  $416.75,  in  8  mo.  21  da.,  at 

15.  $645.39,  in  4  yr.  8  wo.  10  da.9  at 


132  INTEREST. 

328.  To  find  the  principal,  the  amount,  time,  and  rate, 
being  given. 

Ex.     What  principal  will  amount  to  $1880.64,  in  1  yr.  5  mo. 
20  da.,  at  §%  ? 

OPERATION. 

$1.0884)11880.64(1728. 


3.265    )    5641.920  ANALYSIS.  —  The  amounts  of  different 

principals  Tor  the  same  time  and  rate  %  ,  are 
23769  to  each  other  as  the  principals.     One  dollar, 

22855  *n  ^  yr'  ^  mo'  ^  ^a>)  a^  6%  W*H  amount  to 

$1.088£.     To  amount  to  $1880.64,  the  prin- 
cipal  must  be  as  many  times  $1  as  $1.0883 
6530  are  contained  times  in  $1880.64,  or  $1728. 

26120 

26120 

0 

329.  EULE.  —  Divide  the  given  amount  ~by  the  amount  of 
$1  for  the  given  time,  at  the  given  rate. 

EXAMPLES. 

330.  What  principal  will  amount  to 

1.  $1272.254,  in  6  mo.  6  da.,  at  6$? 

2.  $5538.72,  in  8  mo.  12  da.,  at  1%  ? 

3.  $3695.04,  in  1  yr.  4  mo.  18  da.,  at 

4.  $442.71,  in  2  yr.  2  mo.  24  da.,  at 

5.  $14794.31,  in  3  yr.  3  mo.  3  da.,  at  6%  ? 

6.  $1793.38,  in  7  mo.  17  da.,  at  §%  ? 

7.  $1010.65,  in  5  yr.  8  mo.  6  da.,  at  7%  ? 
5.  $977.75,  in  1  yr.  10  mo.  10  da.,  at  6$? 
9.  $1716.75  in  3  yr.  4  mo.  21  ^.,  at  ±%  ? 

70.  $2808.08,  in  2  yr.  8  mo.  12  da.,  at  8%  ? 

./I.  $4312.22,  in  1  yr.  2  mo.  11  flf«.,  at 

12.  $6528.49,  in  4  yr.  7  mo.  6  rfa.,  at 

73.  $1763.02,  in  1  yr.  2  mo.  21  </«.,  at 

1£.  $2457.28,  in  2  ?/r.  5  mo.  23  da.,  at 

75.  $5375.34,  in  1  yr.  6  mo.  15  da.,  at 

76.  $3536.87,  in  2  yr.  7  mo.  10  tfa.,  at 
17.  $4221.50,  in  3  yr.  10  mo.  27  da.,  at 


TRUE    DISCOUNT.  133 


PRESENT  WORTH  AND  TRUE  DISCOUNT. 

331.  The  Present  "Worth  of  a  debt  due  at  some  future  time 
is  its  value  now.     Theoretically,  it  is  such  a  sum  that,  if  placed 
at  interest  to-day  for  the  given  time,  would  amount  to  the  face  of 
the  debt. 

332.  The  True  Discount  is  the  difference  between  the  face 
of  the  debt  and  the  present  worth. 

This  subject  is  an  application  of  the  principle  illustrated  in  Art.  328,  the 
face  of  the  debt  being  the  amount,  the  present  worth  the  principal,  and  the 
true  discount  the  interest. 

In  actual  business,  true  discount  is  little  used,  banks  and  merchants 
generally  using  bank  discount  (355).  True  discount  is  the  interest  on  the 
present  worth  for  the  given  time,  while  bank  discount  is  interest  on  the  face 
of  the  debt.  The  difference  is  therefore  equivalent  to  the  interest  on  the  true 
discount.  For  discount  on  bills,  etc.,  when  time  does  not  enter  in  as  an 
element,  see  Art.  274. 

Ex.  Mr.  B  owes  me  $212,  payable  one  year  from  to-day  with- 
out interest ;  what  is  the  present  worth  of  the  debt,  the  current 
rate  of  interest  being  §%  ? 

ANALYSIS. — Since  $1  in  one  year,  at  6%,  amounts  to  $1.06,  it  would 
require  as  many  dollars  to  amount  to  $212,  as  $1.06  are  contained  times  in 
$212,  or  $200.  The  true  discount  is  $212  -  $200,  or  $12. 

333.  RULE. — /.  To  find  the  present  worth,  divide  the 
face  of  the  debt  by  the  amount  of  $1  for  the  given  time, 
at  the  given  rate. 

II.  To  find  the  true  discount,  subtract  the  present  ivorth 
from  the  face  of  the  debt. 

EXAMPLES. 

334.  The  current  rate  of  interest  being   6$,  what   is  the 
present  worth  and  true  discount  of 

1.  $1000,  due  2  years  hence  ?      3.  $600.  due  in  1  yr.  7  mo.  ? 

2.  $500,  due  in  2  yr.  4  mo.  ?        4.  $800,  due  in  9  mo.  24  da.  ? 
-  5.  $325,  due  in  2  yr.  5  mo.  12  da.  ? 

6.  $175,  due  in  1  yr.  4  mo.  16  da.  ? 

7.  $800,  due  in  5  yr.  8  mo.  22  da.  ? 

8.  $900,  due  in  6  yr.  8  mo.  14  da.  ? 


134  INTEREST. 

9.  Mr.  C.  desiring  to  pay  a  bill  of  $1728  4  months  before  it 
was  due,  was  allowed  a  discount  equivalent  to  the  interest  on  the 
face  of  the  bill  for  the  unexpired  time  at  6%  per  annum  (bank 
discount).     How  much  greater  was  this  discount  than  the  true 
discount  ? 

10.  Goods  to  the  amount  of  $3750  are  sold  on  a  credit  of 
4  months.     For  how  much  cash  could  the  merchant  afford  to  sell 
the  same  goods,  money  being  worth  10$  per  annum  ?    .. 

11.  If  $lpOOO  will  be  due  me  May  28,  and  $8000  May  16,  what 
discount  s^$dld  I  make  on  the  two  claims  Apr.  1,  money  being 
worths^?   / 

REVIEW    EXAMPLES. 

335.     1.  AVhat  is  the  interest  of  $375.60,  for  1  yr.  10  mo. 
16  da.,  at  6%  ? 

2.  What  is  the  amount  of  $1765  for  7  mo.  20  da.,  at  1%  ? 

3.  At  what  rate  will  $1234,  in  2  yr.  2  mo.  26  da.,  produce 
$138.14  interest  ? 

4.  In  what  time  will  $585,  at  6%,  produce  $67.08  interest  ? 

5.  What  principal  will,  in  1  yr.  8  mo.  14  da.,  at  6$,  produce 
$176.22  interest  ? 

6.  The  semi-annual  interest  on  a  mortgage  at  7^  is  $350. 
What  is  the  face  of  the  mortgage  ? 

7.  Mr.  B.  invests  $49500  in  a  business  that  pays  him  $594  per 
month.     What  annual  rate  of  interest  does  he  receive  ? 

8.  Which  is  the  better  investment,  and  what  per  cent.,  one  of 
$8400,  yielding  $336  semi-annually,  or  one  of  $15000,  producing 
$1425  annually  ? 

9.  May  18th,  fa  speculator  bought  1600  bushels  of  wheat,  at 
$1.50  a  bushels/He  afterward  sold  the  whole  for  $2472  cash,  his 
profit  being  equivalent  to  8%  per  annum  on  the  amount  invested. 
What  was  the  date  of  the  sale  ? 

10.  The  par  value  of  Mr.  A.'s  bank  stock  is  $9000,  and  he 
receives  a  semi-annual  dividend  of  $315.     What  per  cent,  is  the 
dividend  per  annum  ? 

11.  Mrs.   C.'s  son  is  now  16  yr.  old;    how  much  must  she 
invest  for  him  at  6$,  that,  on  arriving  at  age,  he  may  have,  with 
simple  interest,  $25000  ? 

12.  What  is  the  interest  of  $10000  for  2  days,  at  6%  per  annum, 
and  a  commission  of  \%  per  day  ? 


REVIEW   EXAMPLES.  135 

13.  A  gentleman  loaned  $15000,  at  6%.     Jan.  1,  1880,  interest 
and  principal   together  equalled  $20000.     When  was  the  money 
loaned  ? 

14.  Find  the  interest  on  $3000,  from  Mar.  16  to  Dec.  4,  at 
6$,  by  the  following  methods  (299) :   1,  ordinary  interest  and 
compound  subtraction  ;  2,  ordinary  interest  and  exact  number  of 
days  ;  3,  accurate  interest. 

15.  Oct.  1,  1880,  the  loans  and  discounts  of  the  National 
Banks  of  the  United  States  amounted  to  $1,041,000,000.     At  6#, 
what  would  be  the  difference  between  the  ordinary  (360  days)  and 
accurate  (365  days)  interest  of  this  amount  for  1  day  ? 

16.  How  much  is  paid  for  the  use  of  $1000  from  Dec.  2  to 
Dec.  17,  accurate  interest  at  6%,  and  a  commission  of  -fa%  per  day 
being  charged  ? 

17.  6%  per  annum  accurate  interest  and  a  bonus  of  •£%%  per 
day  is  equivalent  to  what  rate  per  annum  ? 

-f  18.  A  man  loaned  another  a  sum  of  money,  payable  in 
5  months,  with  interest  at  the  rate  of  6$,  and  at  the  end  of  that 
time  received  $666.25  in  return.  How  much  did  he  loan  ? 

19.  A  speculator  borrowed  $10925  at  6$,  May  16,  1882,  with 
which  he  purchased  flour  at  $6.25  per  barrel.     June  11, 1883,  he 
sold  the  flour  at  $7.50  per  barrel,  cash.     What  did  he  gain  by  the 
transaction  ? 

20.  B  bought  225  A.  24  sq.  rd.  of  land,  Aug.  18,  1882,  at 
$4  an  acre,  borrowing  the  money  to  pay  for  it  at  5$.     He  sold 
the  land  April  7,  1886,  at  an  advance  of  $299.40  on  cost.     If 
meanwhile  he  paid  $46.50  for  taxes  on  the  land,  did  he  gain  or 
lose,  and  how  much  ? 

21.  A  speculator  bought  9000  bu.  grain  at  $1.80  per  bushel, 
Mar.  18,  1875,  the  money  paid  for  it  being  borrowed  at  5J%. 
Dec.  12,  1875,  he  sold  f  of  the  grain  at  $2.00  per  bushel,  and 
the  remainder  at  $1. 90  per  bushel.     What  was  gained  or  lost  by 
the  transaction  ? 

22.  A  person  buying  a  building  lot  for  $5400,  agreed  to  pay  for 
it  in  four  equal  semi-annual  installments,  with  interest  at  6$; 
what  was   the  total  amount  of  money  paid,  the  first  payment 
being  made  at  the  time  of  the  purchase  ? 

23.  A  bill  of  goods  amounting  to  $4316.75  is  due  May  27 ;  how 
much  would  settle  it  May  1  at  6%  ?     How  much  July  3  ? 


136  INTEREST. 

^4.  A  owes  B  £260  9s.  6 J.,  with  interest  at  5%,  for  143  days. 
He  pays  25%  of  the  amount  due  ;  how  much  remains  ? 

NOTE. — In  England,  interest  is  usually  computed  on  the  basis  of  365  days 
to  the  year,  when  the  time  is  given  in  days.  The  legal  rate  in  England  is  5$>. 
To  calculate  interest  on  English  money,  reduce  the  shillings  aud  pence  to  the 
decimal  of  a  pound  (see  Art.  2O4,  Ex.  7,  Note),  apply  any  of  the  methods 
under  Art.  316,  and  reduce  the  resulting  decimal  to  shillings  and  pence. 

Find  the  accurate  interest  of 

25.  £425,  from  Aug.  4  to  Dec.  28,  at  5%. 

26.  £625  125.,  from  Jan.  12  to  Apr.  1,  at  4%. 

27.  £717  16s.  10d.,  from  Mar.  3  to  June  1C,  at 

28.  £429  10s.  8rf.,  from  Sept.  16  to  Nov.  30,  at 

29.  £516  18s.  3d.,  from  Aug.  1  to  Oct.  18,  at 

80.  £612  6s.  lid.,  from  July  1  to  Nov.  3,  at  6%. 

81.  £225  15s.  &d.,  from  Feb.  11  to  Sept.  8,  at  2|-%. 

82.  A  commission  merchant  sold  24160  pounds  of  leather  at 
26f  cents  a  pound,  paid  transportation  $60.40,  cartage  $20,  his 
commission  being  2J%,  and  his  charge  for  inspection  $20.     What 
were  the  net  proceeds  ? 

83.  What  per  cent,  profit  does  a  merchant  make  who  buys  at  a 
discount  of  20,  10,  and  12£%,  and  sells  at  the  list  price  ? 

34.  At  what  per  cent,  above  cost  must  goods  be  marked,  so 
that  when  sold  at  a  discount  of  5%,  there  would  be  a  profit  of  25%  ? 

85.  A  buys  a  bill  of  goods  amounting  to  $2776.40,  on  the  fol- 
lowing terms  : — "4  months,  or  less  5%  cash."     He  accepts  the 
latter,  and  borrows  the  money  at  6%  to  pay  the  bill.     How  much 
does  he  gain  ? 

86.  I  purchase  books  at  $2  each  less  33  J%  and  b%  for  cash. 
What  was  the  net  cost,  and  what  per  cent,  discount  may  be  given 
on  the  list  price  to  produce  a  net  profit  of  10%  ? 

37.  C  of  New  York  sells  for  D  of  Atlanta,  a  quantity  of  cotton, 
amounting  to  $7317.83,  and  charges  a  commission  of  2£%.  By 
instructions,  he  invests  the  proceeds  in  dry  goods,  after  deducting 
a  commission  of  \\%  of  the  amount  expended.  What  was  the 
total  commission? 

88.  A  lawyer  collected  75%  of  an  account  of  $3416,  charging 
5%  commission.  What  amount  should  he  pay  over  ? 

*  When  the  time  is  less  than  1  year,  and  the  rate  is  <b%  or  less,  reject  the  pence,  if 
leas  than  6;  add  1  shilling,  if  more  than  6.    The  result  will  be  sufficiently  accurate. 


ANNUAL    INTEREST.  137 


ANNUAL    INTEREST. 

336.  When  a  note  contains  the  words  "  with  interest  annu- 
ally," the  laws  of  New  Hampshire  and  Vermont,  if  the  interest 
is  not  paid  when  due,  allow  simple  interest  on  the  annual  interests 
from  the  time  they  become  due  to  the  time  of  payment. 

ILLUSTRATION.  — A  agrees  to  pay  B  $6000  in  three  years  from  Jan.  1 , 
1880,  with  interest  annually  at  Q%.  By  this  contract,  $360  becomes  due 
Jan.  1,  1881,  and  on  the  first  day  of  January  in  each  year  thereafter,  until 
paid  ;  this  is  the  "  annual  interest."  Suppose  A  does  not  pay  any  portion  of 
this  interest  until  Jan.  1,  1883,  when  the  principal  becomes  due  ;  then  A,  hav- 
ing had  the  use  of  money  that  his  contract  required  him  to  pay  to  B,  and  B 
having  been  deprived  of  its  use,  B  is  entitled  to  have  simple  interest  added  to 
the  annual  interest,  from  the  time,  when  the  same  became  due  to  Jan.  1, 1883  ; 
so  that  on  Jan.  1,  1883,  B  would  be  entitled  to  the  following  sums  as  interest : 

First  year's  int.  $360  +  2  yrs.  simple  int.  thereon,  $43.20  —  $403.20 
Second "  "  360  +  1  "  "  "  "  21.60  =  381.60 
Third  "  "  360  +  0  (paid  when  due)  00  =  360 

$1080  $64.80  =  $1144.80 

Amount  of  annual  interest $1080.00 

Amount  of  simple  interest  accrued  upon  annual  interest  .  64.80 
Total  amount  of  interest  due $1144.80 

In  calculating  the  simple  int.  upon  the  annual  int.,  shorten  the  operation 
by  finding  the  int.  upon  the  annual  int.  for  the  sum  of  the  several  periods. 

Ex.  What  is  the  amount  due  on  the  following  note  July  1, 
1885? 

$10000.  CONCORD,  N.  H.,  January  1,  1882. 

Three  years  after  date,  for  value  received,  I  promise  to  pay 
A.  B.  THOMPSON,  or  order,  Ten  Thousand  Dollars,  with  interest 
payable  annually. 

C.  A.  DOWNS, 

OPERATION. 

Face  of  note,  on  interest  from  Jan.  1,  1882 $10000.00 

Interest  from  Jan,  1,  1882,  to  July  1, 1885,  3  yr.  6  mo 2100.00 

3  items  of  annual  interest  ($600  each)  are  unpaid : 
1st  from  Jan.  1,  1883,  to  July  1, 1885,        2  yr.  6  mo. 
2nd  from  Jan.  1,  1884,  to  July  1,  1885,        1  yr.  6  mo. 
3rd  from  Jan.  1,  1885,  to  July  1,  1885,  6  mo. 

Int.  on  the  annual  int.  =  int.  ort  $600  for  4  yr.  6  mo 162.00 

Total  amount  duo  July  1,  1885 $12262.00 


138  INTEREST. 

337.  KULE.— To  the  given  principal  and  Us  interest  to 
the  date  of  settlement,  add  the  interest  on  each  annual 
interest  from  the  time  it  is  due  to  the  date  of  settlement. 
The  sum  will  be  the  amount  due  at  annual  interest. 

EXAMPLES. 

338.  1.  At  §%,  interest  payable  annually,  how  much  would 
be  due  Oct.  1,  1884,  according  to  the  laws  of  New  Hampshire,  on 
a  note  of  $8000,  dated  June  1,  1881,  no  payments  having  been 
made  ? 

2.  What  amount  would  be  due  Jan.  1,  1886,  at  6%,  on  a  note 
for  $4200,  dated  Concord,  N.  H.,  May  16,  1882,  interest  payable 
annually,  and  no  payments  having  been  made  ? 

3.  A  note  for  $10000  was  dated  Apr.  1,  1882,  and  payable 
four  years  from  date  without  interest.    Attached  to   this  note 
were   8  notes   of  $400  each  for  the   semi-annual    interest  due 
Oct.  1,  1882,  Apr.  1,  1883,  Oct.  1,  1883,  Apr.  1,  1884,  Oct.  1, 
1884,  Apr.  1,  1885,  Oct.  1,  1885,  Apr.  1,  1886.     How  much  was 
due,  at  8fc,  Apr.  1,  1886,  nothing  having  been  paid  ? 

NOTE. — It  is  the  custom  of  certain  corporations  when  making  loans  for 
long  periods  of  time  on  collateral  security  or  on  bond  and  mortgage,  to  have 
a  note  or  mortgage  given  without  interest  for  the  principal,  and  to  have 
separate  notes  given  for  each  sum  of  annual,  semi-annual,  or  quarterly 
interest,  due  and  maturing  at  the  time  the  interest  is  payable.  These  notes 
draw  interest  after  maturity  like  any  other  note,  and  may  be  collected  without 
disturbing  the  original  loan. 

4.  What  amount  would  be  due  July  1,  1884,  on  a  note  of 
$5000,  dated  July  1,  1882,  given  for  2  years,  with  notes  for  quar- 
terly interest,  no  payments  having  been  made  ? 

5.  Required  the  amount  due  Jan.  1,  1883,  on  a  note  of '$3600, 
dated    Jan.    1,  1881,   due   in   two   years,   notes  for   semi-annual 
interest  from  date,  at  6%,  having  been  given,  and  nothing  having 
been  paid. 

6.  Find  the  amount  of  $1200,  at  6$,  interest  payable  annually, 
from  June   16,    1882,    to    Dec.    28,    1886,   no    interest    having 
been  paid  except  for  the  first  year. 

7.  What  must  be  paid,  Oct.  16,  1885,  in  settlement  of  a  note 
for  $2500,  dated  Manchester,  N.  H.,  May  6, 1880,  said  note  promis- 
ing interest  annually,  and  no  interest  having  been  paid? 


COMPOUND    INTEREST.  139 


COMPOUND     INTEREST. 

339.  Compound  Interest  is  interest  not  only  on  the  prin- 
cipal, but  on  the  interest  also  after  it  becomes  due  (395). 

1.  Interest  |?ay  be  compounded  annually,  semi-annually,  quarterly,  etc. 

2.  Interest  upon  interest  due,  or  compound  interest,  cannot  be  collected 
by  law,  that  is,  payment  cannot  be  enforced  ;  but  such  a  payment  is  equitable, 
and  the  receiving  of  it,  if  the  debtor  is  willing  or  can  be  induced  to  pay  it,  does 
not  constitute  usury  in  the  legal  sense  of  the  word.    In  the  State  of  Missouri, 
parties  may  contract  in  writing  for  the  payment  of  interest  upon  interest,  but 
it  shall  not  be  compounded  oftener  than  once  a  year. 

Ex.     What  is  the  compound  interest  of  $1000  for  3  years, 
at 


OPERATIONS. 

$1000.00     Principal.  Or        $1000 

60.00    Interest  for  1  yr.  1.06 

1060         Amount  for  1  yr.,  or  2d  principal.  1060 

63.60     Interest  of  $1060  for  1  yr.  1.06 

1123.60     Amount  for  2  yr.,  or  3d  principal.  1123.60 

67.416  Interest  of  $1123.60  for  1  yr.  1.06 

1191.016  Amount  for  3  yr.  1191.016 

1000  ___  Original  principal.  1000 

191.016  Compound  interest  for  3  yr.  191.016 

34O.  EULE.  —  Find  the  amount  of  the  given  principal 
for  the  first  period  of  time,  and  make  it  the  principal 
for  the  second.  Find  the  amount  of  the  second  principal 
for  the  second  period  of  time,  and  make  it  the  principal 
for  the  third;  and  so  continue  for  the  whole  time.  The 
last  amount  is  the  amount  required. 

Tlie  last  amount,  less  the  given  principal,  ivill  ~be  the 
compound  interest. 

NOTES.  —  1.  When  the  time  is  not  a  multiple  of  the  interest  period,  find 
the  amount  of  the  principal  to  the  end  of  the  last  period  ;  then  compute  the 
simple  interest  on  this  amount  for  the  remaining  time,  and  add  it  to  the  last 
amount.  The  sum  will  be  the  required  amount. 

2.  The  work  of  computing  compound  interest  may  be  shortened  by  using 
the  tables  on  pages  140  and  141. 


140 


INTEREST. 


341.  Table  showing  the  sum  to  which  $1  will  increase,  at  compound 
interest,  in  any  number  of  years  not  exceeding  45. 


Yrs. 

S*. 

2$*. 

8#. 

81* 

4* 

4tf. 

B*. 

6£. 

W. 

Yrs. 

1 

1.02CO 

1.0250 

1.0390 

1.0350 

1.0400 

1.0450 

1.0500 

1.0600 

1.0700 

1 

2 

1.0404 

1.0506 

1.0609 

1.0712 

1.0816 

1.0920 

1.1025 

1.1236 

1.1449 

2 

3 

1.0612 

1.0769 

1.0927 

1.1087 

1.1249 

1.1412 

1.1576 

1.1910 

1.2250 

3 

4 

1.0824 

1.1038 

1.1255 

1.1475 

1.1699 

11925 

1.2155 

1.2625 

1.3108 

4 

5 

1.1041 

1.1314 

1.1593 

1.1877 

1.2167 

1.2462 

1.2763 

1.3382 

1.4026 

5 

6 

1.1202 

1.1597 

1.1941 

1.2293 

1.2653 

1.3023 

1.3401 

1.4185 

1.5007 

6 

7 

1.1437 

1.1887 

1.2299 

1.2723 

1.3159 

1.3609 

1.4071 

1.5036 

1.6058 

7 

8 

.171? 

1.2184 

1.26-J8 

1.3168 

1.3686 

1.4221 

1.4775 

1.5938 

1  7182 

8 

9 

.1950 

1.2489 

1,3048 

1.3629 

1.4233 

1.4861 

1.5513 

1.6895 

1.8385 

9 

10 

.2190. 

1.2801 

1.3439 

1.4106 

1.4802 

1.5530 

1.0289 

1.7908 

1.9672 

10 

11 

.2434 

1.3121 

1.3842 

1.4600 

1.5395 

1.6229 

1.7103 

1.8983 

2.1049 

11 

If 

.2682 

1.3449 

1.4258 

1.511.1 

1.6310 

1.6959 

1.7956 

2.0122 

2.2522 

12 

13 

.2936 

1.3785 

1.4685 

1.5640 

1.6651 

1.7722 

1.8856 

2.1329 

2.4098 

13 

14 

.3195 

1.4130 

1.5126 

1.6187 

1.7317 

1.8519 

1.9799 

2.2609 

2.C785 

14 

15 

.3459 

1.4483 

1.5580 

1.6753 

1.8009 

1.9353 

2.0789 

2  3966 

2-7590 

15 

16 

1.3728 

1.4845 

1.6047 

1.7340 

1.8730 

2.0224 

2.1829 

2.5404 

2.9522 

16 

17 

1.4002 

1.5216 

1.6528 

1.7947 

1.9479 

2.1134 

2.2920 

2.6928 

3.1588 

17 

18 

1.4282 

1.5597 

1.7024 

1.8575 

2.0258 

2.2085 

2.40(56 

2.8543 

3,3799 

18 

19 

1.4568 

1.5987 

1.7535 

1.92-25 

2.1068 

2.3079 

2.5270 

3.0256 

3.6165 

19 

20 

1.4859 

1.6386 

1.8061 

1.9898 

2.1911 

2.4117* 

2.6533 

3.2071 

3.8697 

20  '. 

21 

1.5157 

1.6796 

1.8603 

20594 

2/.7S8 

2.5202 

2.7S60 

3.3996 

4.1406 

21 

22 

1.5460 

1.7216 

1.9161 

2.1315 

2.3(599 

2.6337 

2.9253 

3.6035 

4.4304 

22 

23 

1.5769 

1.7646 

1.9736 

2.2061 

2.4647 

2.7522 

3.0715 

3.8197 

4.7405 

23 

24 

1.6084 

1.8087 

2.0328 

2.2833 

25633 

2.8760 

3.2251 

4.0489 

5.0724 

24 

23 

1.6406 

18539 

2.0938 

2.3G32 

2<0658 

3.0054 

3.3864 

4.2919 

5.4274 

25 

25 

1.6734 

1.9003 

2.1566 

2.4460 

2.7725 

3.1407 

3.5557 

4.5494 

5.8074 

26 

27 

1.7069 

1.9478 

2.2213 

2.5316 

2.8834 

3.2320 

3.7335 

4.8223 

6.  2139 

27 

28 

1.7410 

1.9965 

2.2379 

2.6202 

2.9987 

3.4297 

3.9201 

5.1117 

6.6488 

28 

23 

1.7758 

2.0464 

2.3566 

2.7119 

3.1187 

3.5840 

4.1161 

5.4184 

7.1143 

29 

30 

1.8114 

2.0976 

2.4273 

2.8068 

3..  434 

3.7453 

4.3219 

5.7435 

7.6123 

30 

31 

18476 

2.1500 

2.5001 

2.S050 

3.3731 

3.9139 

4.5380 

6.0881 

8.1451 

31 

32 

1.8345 

2.2038 

2.5751 

3.0067 

3.5081 

4.0900 

4.7C49 

6.4534 

8.7153 

32 

33 

1.9222 

2.2589 

2.6523 

3.1119 

3.6484 

4.2740 

5.0031 

6.8406 

9.3253 

33 

34 

1.9807 

2.3153 

2.7319 

3.2209 

3.7943 

4.4664 

5.2503 

7.2510 

9.9781 

34 

35 

1.9999 

2.3732 

2  8139 

3.3336 

3.9461 

4.6673 

5.5160 

7.6861 

10.6766 

35 

36 

2.0399 

24325 

28983 

3.4593 

4.1039 

4.8774 

5.7918 

8.1473 

11.4239 

36 

37 

2.0807 

2.4933 

2.9852 

3.5710 

4.2681 

5.0969 

6.0814 

8.6361 

12.2236 

37 

38 

2.1223 

2.5557 

3.0748 

3.6960 

4.4388 

5.3262 

6.3855 

9.1543 

13.0793 

38 

39 

2.1647 

2.6195 

3.1670 

3.8254 

4.6164 

5.5659 

6.7048 

9.7035 

13.9948 

39 

40 

2.2080 

2.6851 

3.2620 

3.9593 

4.8010 

5.8164 

7.0400 

10.2857 

14.9745 

40 

41 

2.2522. 

2.7522 

3.3599 

4.0978 

49931 

6.0781'v- 

i,7.3920 

10.9029 

16.0227 

41 

42 

2.2972 

2.8210 

34607 

4.2413 

5.1928 

6.3516  ' 

*7.7616 

11.5570 

17.1443 

42 

43 

2.3432 

2.8915 

3.5645 

4.3897 

54005 

6.6374 

8.1497 

12.2503 

18.3444 

43 

44 

2.3901 

2.9638 

3.6715 

4.5433 

5.6165 

6.9361 

8.5572 

12.9855 

19.6285 

44 

45 

2.43T9 

3.0379 

3.7816 

4.7024 

5.8412 

7.2482 

8.9850 

13.7646 

21.00x5 

45 

To  find  the  sum  to  which  a  given  amount  will  increase,  at  compound  interest,  at  any  of 
the  rates  per  cent,  and  number  of  years  expressed  in  the  above  Table  : 

Multiply  the  given  amount  by  the  sum  to  which  one  dollar  will  increase  at  the  rate  and 
for  the  number  of  years  required,  marking  off  as  many  decimals  from  the  product  as  there 
are  decimals  in  the  multiplier  and  multiplicand. 

NOTES. — 1.  The  amount  for  any  number  of  years  not  given  in  the  table  may  tie  computed 
by  finding  the  product  for  any  two  numbers  of  years  whose  sum  equals  the  given  time.  Thus, 
the  compound  amount  of  $1  at  §%  for  55  years,  may  be  found  by  multiplying  $13.7646,  the 
amount  for  45  years,  by  1.7908,  the  amount  for  10  years. 

2.  If  the  interest  is  compounded  semi-annually,  to  find  the  amount  from  the  table,  take 
twice  the  number  of  years  at  one-half  the  rate.    Thus,  the  amount  at  8£,  compounded  semi- 
annually,  for  5  years,  is  equivalent  to  the  amount  for  10  periods  of  6  months  each,  at  4.%  for 
each  period,  and  is  the  same  as  the  amount  for  10  years  at  4%.    If  the  interest  is  compounded 
quarterly,  take  4  times  the  number  of  years  at  one-fourth  the  rate. 

3.  The  compound  interest  of  Sjjjl  is  $1  less  than  the  amounts  in  the  above  table. 


v> 


)  vA  rxO  ' 
COMPOUND    INTEREST. 


5 


141 


342.  Table  showing  the  sum  to  which  $1,  prdd  at  the  beginning  of  each 
year  will  increase  at  compound  interest,  in  any  number  of  years  not  exceeding  50. 


Yrs. 

8jt. 

Stf. 

4*. 

5*. 

6*. 

7* 

8*. 

10*. 

Yrs. 

1 

1.0300 

1.0350 

1.0400 

1.0500 

1.0600 

1.0700 

10800 

1.1000 

1 

2 

2.0909 

2.1062 

2.1216 

2.1525 

2.1835 

2.2149 

22464 

2.3100 

2 

3 

3.1836 

3.2149 

3.2485 

3.3101 

3,3746 

3.4399 

3.5061 

3.6410    3 

4 

4.3091 

4.362) 

4.4163 

4.5256 

4.6371 

4.7507 

4.8666 

51051 

4 

5 

6.4634 

5.5502 

5.6330 

5.8019 

5.9753 

6.1533 

6.3359 

6.7156 

5 

G 

6.6625 

6.7791 

6.8933 

7.1420 

7.S938 

7.6540 

7.9228 

8.4872 

6 

7 

7.8923 

8.0517 

8.2142 

8.5491 

8.8975 

9.2598 

9.6366 

10.4359 

7 

8 

9.1591 

9.3685 

9.5828 

1C.0286 

10.4913 

10.9780 

11.4876 

12.5795 

8 

9 

10.4633 

10  7314 

11.0061 

11.5779 

12.1803 

12.8164 

13.4866 

14.9374 

9 

10 

11.8078 

12.1420 

12.4334 

13.2083 

13.9716 

14.7836 

15.6455 

17.5312 

10 

11 

131920 

13.6020 

140258 

14.9171 

15.8699 

16.8885 

17.9771 

23.3843 

11 

12 

14.6178 

15  1130 

15.6288 

16.7130 

17.8321 

19.1406 

20.4952 

23.5227 

12 

13 

16.0863 

16.6770 

17.2919 

18.5983 

20.0151 

21.55J5 

23.2149 

26.9750 

13 

14 

17.5989 

18.2957 

19.0135 

20.5786 

22.2780 

24.1290 

26.1521 

80.7725 

14 

15 

19.1569 

19.  9  no 

20.8.245 

22.6575 

JJ6.88S1 

29.3243 

34.9497 

15 

16 

20.7816 

21.7050 

22.6975 

24.8434 

27  21-39 

^29.8402 

32.7502 

39,5447 

16 

17 

22.4144 

23.4997 

24.6454 

27.1324 

29^9057 

32.9390 

36.4502 

44.5992 

17 

18 

24.1169 

25.3573 

266712 

29.5390 

32.7600 

36.3790 

40.4463 

50.1591 

18 

19 

25.8704 

27.2797 

28.7781 

32.0630 

35.7856 

39.9955 

44.7620 

56.2750 

19 

20 

27.6765 

29.2695 

30.9692 

34  7193 

38.9927 

43.8652 

49.4229 

63.0025 

20 

21 

29.5368 

31.3290 

33.2480 

37.5352 

42.3923 

48.0058 

54.4568 

70.4027 

21 

21 

31.4529 

33.4634 

35.6179 

40.43)5 

45.9J58 

52.4561 

59.8968 

785430 

22 

SB 

33.4-265 

35  6365 

38.0826 

43.5023 

43.8156 

57.1767 

65.7648 

87.4973 

23 

34 

35.4393 

37.9499 

40.6459 

46.7271 

53.8645 

62.249  ) 

72.1059 

97.3471 

24 

25 

37.5530 

40.3131 

43.3117 

50.1135 

58.1564 

67.6765 

18.9544 

108-1818 

25 

26 

39.7096 

42.7591 

46.0342 

53.6931 

62.7058 

73.4838 

86.3508 

120.0999 

26 

27 

41.9309 

45.2908 

48.9576 

57.40  }6 

67.5281 

79.6977 

94.33h8 

133.2099 

27 

28 

44.2138 

47.9103 

51.9603 

61.3227 

72.6393 

86.3465 

102.9659 

147.6309 

» 

29 

46.575* 

50.6227 

55.0349 

65.4338 

78.0592 

93.4608 

112.2a32 

163.4940 

29 

30 

49.0027 

53-4295 

53.3283 

69.7638 

83.8017 

101.0730 

122.3459 

180.9434 

30 

31 

51.5028 

56.3345 

61.7015 

74.2933 

898898 

109.2182 

1&3.2135 

200.1378 

31 

32 

54.0778 

59.341  1 

65  2035 

79.0838 

96.3432 

117.9334 

144.9506 

221.2515 

32 

33 

56.7302 

62.4532 

68.8579 

84.0670 

03.1838 

127.2583 

157.6267 

244.4767 

33 

34 

59.4621 

65.6743 

72.6522 

89.3203 

10.4348 

137.2369 

171.3168 

270.0244 

34 

35 

62.2719 

69.0076 

76.59*3 

94.8383 

118.1209 

147.9135 

186.1021 

298.1268 

35 

36 

65.1742 

72.4579 

80  7022 

100.6231 

126.2681  159.3374 

202.0703 

329.0395 

36 

37 

68.1594 

76.0239 

84.9703  106.7095 

134.9042  '171.5610 

219.3159 

868.0484 

37 

38 

71.2342 

79.7.249 

89.4091  113.0950 

144.0535  184.6403 

237.9412 

400.4478 

33 

39 

74.4013 

83.5503 

94.0255  119.7998 

153.7620  198.6351 

258.0565 

441.5926 

39 

40 

77.6633 

87.509J 

98.8235  126.8393  164.0477  213.6096 

279.7810 

486.8518 

40 

41 

81.  Or  2 

91.6074 

103.8196  134.2318  174.9506  229.6322 

303.2435 

536.6370 

41 

42 

84.4839 

95.8486 

109.0124  141.9933  136.5076  246.7765 

328.5830 

591.4007 

42 

43 

88.0484 

100.2383 

114.4129  150.1430  |198.75.Sf)  265.1208 

355.9496 

651.6408 

43 

44 

91.7199 

104.7817 

120.0294  ,158.7002  211  7435  284.7493 

385.5056 

717.9048 

44 

45 

95.5015 

109  4340 

1258706  167.6852 

225.5081  305.7518 

417.4261 

790.7953 

45 

46 

99.3965 

114.3510 

131.9454 

1771194 

240.0986  328,2244 

451.9002 

870.9749 

46 

47 

103.4084 

119.3383 

138.2632  137.0254 

255.5645  352.2701 

489.1322 

959.  1723 

47 

48 

107.5406 

124.6018 

144.8337  197.4267 

271.9584  377.9930 

529.3427 

1056-  1P96 

48 

49 

111  7963 

129.9979 

151.6671  i208.3480 

289.3359  1405.5389 

572.7702 

1162.9085 

49 

50 

116.1307 

135.5328 

158.7738  219.8154 

307.7561  434.9859 

619.6718 

1280.2993 

53 

To  find  the  sum  to  which  a  given  amount,  per  annum,  will  increase  at  compound  inter- 
est, at  any  of  the  rates  per  cent,  and  number  of  years  expressed  in  the  above  Table  : 

Multiply  the  given  amount,  per  annum,  by  the  sum  to  which  one  dollar  per  annum  will 
increase  at  the  rate  and  for  the  number  of  years  required,  marking  off  as  many  decimals  from 
the  product  as  there  are  decimals  in  the  multiplier  and  multiplicand. 

NOTE. — If  the  amount  be  payable  semi-annually,  and  compound  interest  is  to  be  allowed 
semi-annually,  take  the  amount  for  double  the  number  of  years  at  one-half  the  rate  per  cent. 
Thus,  for  a  semi-annual  payment  of  $1  for  10  years  at  10  per  cent.,  take  the  amount  of  $1  for 
20  years  at  5  per  cent.  =  $34.7193.  For  a  quarterly  payment,  take  the  amount  for  four  times 
the  number  of  years  at  one -fourth  the  rate  per  cent. 


142  INTEREST. 

EXAM  PLES. 

343.  1.  What  will  $450  amount  to  at  compound  interest,  in 
4  years,  compounded  annually  at  4%  ?  At  3%  ? 

2.  Find  the  compound  interest  of  $360,  for  2  years,  interest 
compounded  semi-annually  at  §%.  At  5%. 

&  What  is  the  compound  interest  of  $800  for  1  yr.  3  mo.  at 
8$,  interest  compounded  quarterly  ? 

4.  At  compound  interest,  what  is  the  amount  of  $1728  for  3  yr, 
4  mo.  16  $B.,  interest  compounded  annually  at  3%  ?    At  6%  ? 

NOTE. — First  find  the  amount  for  3  years,  and  uss  this  amount  as  the 
principal  for  the  remaining  time. 

5.  B  holds  a  mortgage  against  A's  property  dated  Apr.  1, 1881, 
for  $20000,  interest  payable  annually  at  6%.     The  interest  due 
Apr.  1,  1882,  is  not  paid  until  May  26,  1882.     How  much  is  then 
due,  A  having  consented  to  pay  interest  upon  interest  ?      (See 
Note  2,  Art.  339). 

NOTE. — In  solving  the  following  examples,  uso  the  tables  in  Art.  34 1  - 
342. 

6.  A  gentleman   deposits  in  a   savings  bank  $100  when  his 
child  is  one  year  old.     How  much  will  this  amount  to  when  he  is 
21  years  old,  interest  being  compounded  semi-annually  at  4%? 
At  5#? 

7.  If  at  the  age  of  25  years,  a  person  places  $2000  on  interest, 
compounded  annually  at  6$,  what  will  be  the  amount  due  him 
when  he  is  50  years  old  ? 

8.  What  will  $625  amount  to  at  compound  interest,  in  36  years, 
compounded  annually  at  3%  ?     At  4%  ? 

9.  At  the  age  of  20,  and  every  year  thereafter,  a  young  man 
places  $200  at  compound  interest  at  Q%.     How  much  will  he  have 
at  the  age  of  30  ?    At  the  age  of  40  ?     (See  Art.  343.) 

10.  How  much  will  a  gentleman  have  at  the  end  of  three  years, 
if  he  places  at  compound  interest  at  5%,  $300  at  the  beginning 
of  each  year  ? 

11.  Mr.  B.,  whose  life  is  insured  for  $4000,  pays  an  annual 
premium  of  $114.     How  much  would  this  amount  to  at  6^  com- 
pound interest  in  20  years  ? 

12.  A  lady  deposits  $50  in  a  savings  bank  Jan.  1  and  July  1, 
of  each  year;  how  much  will  be  placed  to  her  credit  in  15  years, 
money  being  worth  6%,  compound  interest  ? 


COMMERCIAL    PAPER.  143 

13.  What  sum  must  be  placed  at  compound  interest,  at  6^,  to 
amount  to  $1000  in  5  years? 

NOTE. — In  compound  interest,  as  in  simple  interest,  the  amounts  are 
proportional  to  the  principals;  hence  the  amount  of  any  principal  is  as  many 
times  greater  than  the  amount  of  $1,  as  that  principal  is  greater  than  $1. 

To  find  the  principal,  divide  the  given  amount  by  the  amount  of  $1  for 
the  given  time  and  rate. 

In  simple  interest,  the  interest  on  a  given  principal  for  a  given  time  is  in 
proportion  to  the  rate  per  cent.,  and  at  a  given  rate,  in  proportion  to  the  time  ; 
but,  in  compound  interest,  such  is  not  the  case.  If  the  rate  or  time  be  doubled, 
the  interest  is  more  than  doubled. 

14-  How  much  should  a  gentleman  invest  at  compound  inter- 
est, 6^,  for  his  son  who  is  now  G  years  old,  so  that,  when  he  becomes 
21  years  of  age,  he  may  have  $10000  ? 

15.,  In  the  above  example,  how  much  should  be  invested  at  the 
beginning  of  each  year  to  produce  the  same  sum? 

16.  A  gentleman  at  his  death  left  $7350  for  the  benefit  of  his 
only  son,  12  years  old,  the  money  to  be  paid  to  him  when  he 
should  be  21  years  of  age.     How  much  did  he  receive,  interest  at 
6%,  compounded  send-annually  ? 

17.  How  much  must  a  person  at  the  age  of  25  years,  place  at 
compound  interest  at  6$,  so  that  the  amount  due  him,  when  he 
is  50  years  old,  will  be  $20000  ? 

18.  In  the  above  example,  how  much  should  he  invest  annually 
to  produce  the  same  sum? 


COMMERCIAL    PAPER. 

344.  Commercial  Paper  embraces  notes,  drafts,  bills  of 
exchange,  etc. 

345.  A  Note  (also  called  a  Promissory  Note)  is  a  written 
promise  to  pay  a  certain  sum  of  money  on  demand  or  at  a  specified 
time. 

346.  The  Maker  of  a  note  is  the  person  who  signs  it,  and 
thus  becomes  responsible  for  its  payment.      The  Payee  is  the 
person  to  whom,  or  to  whose  order,  it  is  made  payable.     The 
Face  of  a  note  is  the  sum  promised. 

In  Note  1,  Art.  352,  Peter  Cooper  is  the  maker  ;  George  Peabody  is  the 
payee  ;  the  face  of  the  note  is  $100U. 


r 


144  INTEREST. 

347.  A  Negotiable  Note  is  a  note  which  is  made  payable  to 
bearer  or  to  the  order  of  some  person  (See  Notes,  Art.  352). 

1.  A  note  is  non-negotiable  when  it  is  payable  only  to  the  party  named  in 
the  note. 

2.  A  negotiable  note  made  in  New  Jersey  must  contain  the  words  "  with- 
out defalcation  or  discount ;  "  in  Missouri,  the  words  "  negotiable  and  payable 
without  defalcation  or  discount." 

3.  Negotiable  notes  payable  to  order  may  be  sold  or  transferred  by  the 
payee  writing  his  name  upon  the  back  of  the  note.     He  then  becomes  an 
indorser. 

348.  The  Indorser  of  a  note  or  draft  is  the  person  who 
writes  his  name  on  the  back  of  it,  and  by  so  doing  guarantees 
its  payment. 

If  Mr.  Erastus  Corning  desires  to  sell  or,|ransfer  Note  3,  Art.  352,  it 
will  be  necessary  for  him  to  indorse  it.  If  he  writes  his  name  only,  it  is  called 
an  indorsement  in  blank,  and  the  note  is  then  payable  without  further  indorse- 
ment to  any  person  lawfully  holding  the  same.  He  may  indorse  it  in  full  by 
making  it  payable  to  a  particular  person,  thus — "  Pay  to  the  order  of  Henry 
R.  Pierson,  Erastus  Corning."  Before  it  can  be  again  transferred,  it  will 
require  the  indorsement  of  Henry  R.  Pierson.  For  greater  security,  checks, 
notes,  drafts,  etc.,  are  indorsed  in  full  when  sent  by  mail. 

If  an  indorser  does  not  wish  to  guarantee  the  payment  of  a  note,  draft, 
etc.,  he  writes  "  Without  recourse  "  over  his  name  at  the  time  of  the  indorse- 
ment. 

Sometimes  notes  and  drafts  are  drawn  to  the  order  of  the  maker  or  the 
drawer  (to  the  order  of  myself  or  ourselves)  to  facilitate  their  transfer  without 
the  indorsement  of  the  holder. 

349.  A  Draft,  or  Bill  of  Exchange  is  an  order  or  request 
addressed  by  one  person  to  another  directing  the  payment  of  a 
specified  sum  of  money  to  a  third  person  or  to  his  order. 

350.  The  Drawer  of  the  draft  is  the  person  who  signs  it. 
The  Drawee  is  the  person  on  whom  it  is  drawn.     The  Payee 
is  the  person  to  whom,  or  to  whose  order,  it  is  made  payable. 

In  Draft  5,  Art.  352,  C.  P.  Huntington  is  the  drawer ;  Drexel,  Morgan 
&  Co.  are  the  drawees ;  J.  &  W.  Seligman  &  Co.  are  the  payees. 

1.  The  person  in  whose  favor  the  bill  is  drawn  is  sometimes  called  the 
buyer,  and  becomes  the  "  remitter."     After  the  bill  is  presented  and  accepted, 
the  drawee  is  called  the  acceptor,  and  the  draft,  an  acceptance.     The  draft 
then  has  the  same  legal  significance  as  a  promissory  note. 

2.  A  person  accepts  or  promises  to  pay  a  draft  by  writing  the  word 
"  Accepted"  and  the  date  over  his  name  across  its  face. 


COMMERCIAL    PAPER.  145 

3.  Drafts  are  sometimes  accepted  in  the  following  form  :  —  "Accepted 
August  20,  1881,  and  payable  at  the  National  Park  Bank,  New  York,  G.  B. 
Horton  &  Co. " 

4.  In  the  State  of  New  York,  both  by  law  and  custom,  the  drawee  of  a 
draft  may  demand  24  hours  consideration  from  the  time  the  draft  is  presented 
for  acceptance. 

When  accepted,  it  must  bear  the  date  when  first  seen  by  him. 

5.  To  "  honor  "  a  draft  is  to  accept  it  or  pay  it  on  being  presented. 

351.  A  Protest  is  a  formal  statement  made  by  a  Notary  Public, 
declaring  that  a  draft  or  note  has  been  presented  for  payment  or 
acceptance,  and  was  refused. 

352.     FORMS  OF   NOTES  AND   DRAFTS. 

1.  DEMAND  NOTE. 
$1000.  NEW  YORK,  August  19,  1881. 

On  demand,  I  promise  to  pay  GEOKGE  PEABODY,  or  bearer, 
One  Thousand  Dollars.  Value  received. 

PETER  COOPER. 

The  above  note  is  payable  on  demand, — that  is,  whenever  presented  ;  is 
negotiable  (payable  to  bearer) ;  and  bears  interest  from  date  at  the  legal  rate 
of  the  State  in  which  it  is  made.  If  the  words  "  or  bearer  "  were  omitted  the 
note  would  not  be  negotiable. 

2.  TIME  NOTE — INTEREST-BEARING. 

$875^.  CINCINNATI,  OHIO,  July  16,  1882. 

Six  months  after  date,  I  promise  to  pay  GEO.  C.  MILLER, 
or  order,  Eight  Hundred  Seventy-five  and  -£fa  Dollars,  with 
interest  at  eight  per  cent.  Value  received. 

ALEX.  MCDONALD. 

The  above  note  is  payable  6  mo.  3  da.  after  its  date,  or  Jan.  19,  1883  ; 
is  negotiable  (payable  to  order)  ;  and  draws  interest  from  its  date  at  8%  per 
annum.  If  the  rate  of  interest  was  omitted,  it  would  bear  interest  at  the 
legal  rate  of  the  State  for  such  cases,  6^.  (See  Art.  298.) 

3.  TIME  NOTE— WITHOUT  INTEREST  -  PAYABLE  AT  A  BANK. 
$6000.  ALBANY,  N.  Y.,  December  4,  1881. 

Sixty  days  after  date,  I  promise  to  pay  to  the  order  of  ERASTUS 
CORNING,  Six  Thousand  Dollars,  at  the  Second  National  Bank. 

Value  received. 

E.  C.  KOONZ. 


146  INTEREST. 

The  preceding  note  is  payable  63  days  from  Dec.  4,  1881,  or  Feb.  5,  1882. 
It  is  payable  at  the  Second  National  Ban1!!.  No  interest  will  be  due  at  maturity 
(Feb.  5).  If  the  note  is  not  paid  at  maturity,  it  will  bear  interest  from 
that  date. 

4.  JOINT  AND  SEVERAL  NOTE. 

$^16^-  WORCESTER,  MASS,  May  27,  1882. 

Four  months  after  date,  we  jointly  and  severally  promise  to 
pay  JOHN  S.  BALLARD  &  Co.,  or  order,  Four  Hundred  Sixteen 
T3^j-  dollars,  with  interest  from  date,  value  received. 

T.  K.  EARLE. 

CHAS.  W.  SMITH. 

If  the  above  note  were  written  "we  jointly  promise,  etc.,"  it  would  be 
called  a  joint  note-  The  makers  of  a  joint  note  must  be  sued  jointly,  each 
being  responsible  for  one-half  of  the  amount  of  the  note.  The  makers  of  a 
joint  and  several  note  may  be  sued  separately,  either  being  responsible  for 
the  full  amount  of  the  note. 

5.  SIGHT  DRAFT. 

$8000.  SAN  FRANCISCO,  CAL.,  May  1,  1882. 

At  sight,  pay  to  ttie  order  of  J.  &  W.  SELIGMAN  &  Co.,  Eight 
Thousand  Dollars,  value  received. 

C.   P.  HUNTINGTON. 

To  DREXEL,  MORGAN  &  Co.,  New  York. 

6.  TIME  DRAFT. 

$5000.  BURLINGTON,  IOWA,  June  18,  1881. 

At  sixty  days'  sight,  pay  to  the  order  of  ADDISON  BALLARD, 
Five  Thousand  Dollars,  value  received,  and  charge  to  account  of 

A.  G.  ADAMS. 

To  BARTON  &  JONES,  Chicago,  111. 

Drafts  are  sometimes  drawn  a  certain  number  of  "  days  after  date." 
For  Foreign  Bills  of  Exchange,  see  Art.  418. 

NOTES. — 1.  A  note  should  contain  the  words  "  Value  received,"  as  a  con- 
tract without  a  consideration  is  not  legally  binding. 

2.  Negotiable  securities  are  good  in  the  hands  of  ono  who  purchases  in 
good  faith  and  before  maturity,   although   the  seller  may  have  found  or 
stolen  them. 

3.  Where  no  place  of  payment  is  specified,  a  promissory  note  is  payable 
at  the  maker's  place  of  business,  or  if  none  is  known,  at  the  residence  of 
the  maker. 


COMMERCIAL    PAPER.  147 

4.  A  note  or  draft  must  be  presented  at  the  place  where  it  is  made  pay- 
able. If  at  a  bank,  during  banking  hours  ;  if  at  a  place  of  business,  during 
business  hours  ;  if  at  a  residence,  during  family  hours  ;  and  if  the  maker,  or 
some  one  for  him,  is  not  ready  with  legal  tender  currency  to  pay  it,  the  holder 
need  not  call  again.  A  check,  even  if  certified,  is  not  a  legal  tender,  and  may 
be  lawfully  refused. 

353.  Days  of  Grace  and  Maturity. — The  day  of  ma- 
turity is  the  day  on  which  a  note  becomes  legally  due. 
According  to  the  laws  of  most  of  the  States,  a  note  is  not  legally 
due  until  three  days  after  the  expiration  of  the  time  specified  in 
the  note,  except  the  note  contain  the  words  "without  grace." 
These  days  are  called  days  of  grace,  but  they  are  of  no  advantage 
to  the  payer,  since  interest  is  charged  for  them  as  for  any  others. 

1.  California  has  abolished  days  of  grace  altogether.     In  Georgia,  Ala- 
bama, and  Kentucky,  grace  is  allowed  on  promisscry  notes  only  in  case  they 
are  made  payable,  or  are  discounted  or  left  for  collection  at  a  bank  or  private 
banker's.    (March,  1879.) 

2.  By  statute  in  the  State  of  New  York  and  most  of  the  States,  all  bills 
and  notes  due  on  Sunday  are  payable  on  Saturday,  and  all  due  on  a  legal 
holiday  are  made  payable  on  the  business  or  secular  day  next  preceding. 
Thus,  if  a  holiday  falls  on  Thursday,  all  notes,  etc.,  must  be  paid  on  Wednes- 
day ;  if  a  holiday  falls  on  Monday,  all  notes  due  Sunday  or  Monday  would 
be  payable  on  Saturday  ;  if  a  holiday  falls  on  Saturday,  notes  due  Saturday  or 
Sunday  would  bo  payable  on  Friday. 

3.  The  legal  holidays  in  the  State  of  New  York  are  New  Year's  Day 
(Jan.  1),  Washington's  Birthday  (Feb.  22),  Decoration  Day  (May  30),  Inde- 
pendence Day  (July  4),  Election  Day  (the  first  Tuesday  after  the  first  Monday 
in  November),  Thanksgiving  Day  (the  day  appointed  by  the  President  of  the 
United   States  and   Governor  of  the   State,  usually  the  last   Thursday  of 
November),  and  Christmas  (Dec.  25). 

4.  When  a  legal   holiday  falls  on  Sunday,  Monday  is,  by  the  statute  of 
New  York,  made  a  legal  holiday,  and  notes,  etc.,  maturing  on  Sunday  or 
Monday,  must  be  paid  on  the  preceding  Saturday. 

5.  A  note  made  due  at  a  fixed  date  in  the  future,  carries  3  days'  grace 
(unless  the  words  "  without  grace  "  are  used  in  the  contract).     Thus,  a  note 
stating  that  "  on  May  1,  1882, 1  promise,  etc.,"  would  carry  3  days'  grace,  and 
would  be  payable  May  4,  1882. 

6.  When  the  time  of  a  note  is  expressed  in  months,  calendar  months  are 
used  to  determine  the  day  of  maturity  ;  when  in  days,  the  exact  number  of 
days  is  used. 

Thus,  a  note  dated  July  16,  and  payable  two  months  from  date,  would 
nominally  mature  Sept.  16,  and,  including  the  three  days  of  grace,  would 
legally  mature  Sept.  19.  A  note  having  the  same  date,  and  payable 


148  INTEREST. 

sixty  days  from  date,  would  nominally  mature  Sept.  14,  and,  including  the 
three  days  of  grace,  would  legally  mature  Sept.  17. 

7.  A  note  due  in  one  or  more  months  from  date,  matures  on  the  corres- 
ponding day  of  the  month  up  to  which  it  is  reckoned,  if  there  are  so  many 
days  in  that  month ;  but  if  not  so  many,  it  then  matures  on  the  last  day  of 
said  month,  to  which  the   usual  grace  must  be  added.     Thus,  notes  dated 
Jan.  28,  29,  30,  or  31,  and  payable  one  month  from  date,  would  become  due 
Mar.  3  (Feb.  28  with  3  days'  grace  added). 

8.  When  drafts  are  payable  a  certain  time  after  sight,  the  date  of  accept- 
ance and  the  time  of  the  draft  determine  the  day  of  maturity.     Thus,  if  a  draft 
is  dated  May  16,  accepted  May  20,  and  payable  sixty  days  after  sight,  it  would 
mature  or  be  due  63  (including  3  days  of  grace)  days  after  May  20,  or  July  22. 
If  payable  60  days  after  date,  it  would  mature  63  days  after  May  16/or  July  18. 
It  is  not  necessary  to  present  for  acceptance  drafts  drawn  a  certain  time  after 
date,  but  as  a  courtesy  to  the  drawee,  it  is  usually  done. 

9.  Days  of  grace  are  allowed  on  drafts  according  to  the  custom  of  the 
place  where  they  are  payable.     The  statute  of  New  York  forbids  grace  on  all 
sight  drafts,  no  matter  on  whom  drawn,  and  on  all  time  drafts  which  appear 
on  their  face  to  be  drawn  "  upon  any  bank,  or  upon  any  banking  association 
or  individual  banker,  carrying  on  the   banking  business   under  the  act  to 
authorize  the  business  of  banking." 

EXAMPLES. 

354.  1.  How  much  would  be  due  on  Note  1,  Art.  352, 
Jan.  1,  1882,  finding  the  time  by  compound  subtraction  ? 

2.  How  much  would  be  due  on  Note  2,  Art.  352,  at  its  matu- 
rity? How  much  March  1,  1883  ?  Supposing  the  rate  of  interest 
was  omitted  in  the  note,  how  much  would  be  due  May  4,  1883  ? 

8.  Ninety  days  after  June  21  is  what  date  ? 

OPEKATIONS.  ANALYSIS. — Subtract  from  the  given 

90  Or     9     June.          number  of  days,  the  number  of  days  re- 

9     June.  31     July.  maining  in  June,  and  from  this  remainder, 

~  3-^     Aug.  subtract  successively  the  number  of  days 

in  the  following  months  until  the  remain- 

31      July.  <jer  js  equai  to  or  less  than  the  number  of 

50  90  days  in  the  next  following  month.     The 

31      Au£  19      Sept  last  remain(ier  represents  the    required 

date. 
19     Sept.  Or,  write  the  remaining  number  of 

days  in  June,  and  the   number  of  days 

in  a  sufficient  number  of  months  to  produce  about  the  given  number  of  days. 
Take  their  sum  and  subtract  it  (if  possible)  from  the  given  number  of  days. 
The  remainder  will  be  the  day  of  the  following  month  representing  the 
required  date.  If  the  sum  is  greater  than  the  given  number,  subtract  the 


BANK    DISCOUNT.  149 

excess  from  the  number  of  days  in  the  last  month  written.     The  remainder 
will  be  the  required  date. 

If  the  time  be  30,  60,  or  90  days,  regard  each  30  days  as  a  calendar  month, 
and  correct  by  subtracting  1  day  for  each  intervening  month  containing  31 
days,  and  adding  2  days  for  February  (in  leap  year  1  day).  Thus  3  months 
after  June  21  is  Sept.  21,  and  by  subtracting  2  days  for  July  and  August,  the 
correct  result  is  Sept.  19. 

4.  Supposing  Note  3,  Art.  352,  was  payable  90  days  from 
date,  what  would  be  its  due  date  ?     The  note  as  given  not  being 
paid  at  maturity,  how  much  would  be  due  Feb.  25,  1882,  protest 
fees  $2.10? 

5.  How  much  would  settle  Note  4,  Art.  353,  Dec.  30,  1882? 

6.  If  Draft  6,  Art.  352,  was  accepted  June  19, 1881,  what  was 
the  date  of  maturity? 


BANK     DISCOUNT. 

355.  Bank  Discount  is  simple  interest  of  a  note,  paid  in 
advance,  for  the  number  of  days  the  note  has  to  run.     It  may  be 
computed  by  any  of  the  methods  given  for  simple  interest. 

On  notes  without  interest  (the  usual  case  of  notes  discounted  at  banks), 
bank  discount  is  reckoned  on  their  face,  the  amount  due  at  maturity ;  on  notes 
with  interest,  it  is  reckoned  on  the  amount  due  at  maturity,  or  their  face  plus 
the  interest  for  the  full  time  of  the  note. 

356.  The  Proceeds  of  a  note  is  the  amount  received  by  the 
holder  from  the  bank  when  the  note  is  discounted.     It  is  the 
amount  on  which  the  discount  is  reckoned  less  the  discount. 

357.  Call  Loans. — Banks  in  the   City  of  New  York  loan 
large  amounts  of  money  upon  stocks,  bonds,  etc.,  as  collateral 
security,  payable  on  demand  or  on  giving  one  day's  notice.     Such 
loans  are  called  "call"  or  demand  loans,  and  interest  on  them  is 
paid  at  the  end  of  the  time. 

358.  The  time  to  be  reckoned  on  a  loan  or  note  is  exclusive 
of  the  day  of  date,  but  includes  the  day  of  maturity  or  payment. 
Thus,  in  discounting  a  note  in  the  City  of  New  York,  Apr.  4, 
which  would  mature  Apr.  24,  the  discount  would  be  calculated  for 

20  days. 


150  INTEREST. 

In  Philadelphia,  Baltimore  and  other  cities  it  is  the  custom  of  banks  in 
finding  time  to  include  both  the  da}-  of  discount  and  the  day  of  maturity. 
Thus,  the  discount  on  the  above  note  would  be  reckoned  for  21  days. 

359.  Banks  of  the  City  of  New  York  reckon  discount  both 
on  the  basis  of  360  and  365  days  to  the  year. 

NOTE. — In  April  1880,  the  author  made  a  personal  investigation  of  this 
subject  among  the  70  banks  of  the  City  of  New  York,  and  found  that  their 
methods  were  not  uniform  ;  some  banks  reckoning  discount  on  the  basis  of 
865  days  to  the  year,  and  others  on  the  basis  of  360  days.  It  is  the  custom  of 
brokers  and  dealers  in  commercial  paper  to  reckon  interest  and  discount  on 
the  basis  of  360  days  to  the  year.  Below  are  given  extracts  from  letters 
received  from  some  of  the  above  banks. 

"  In  discounting  notes,  we  reckon  interest  on  the  basis  of  365  days  to  the  year  when  at 
6#;  360  when  at  a  rate  lower  than  legal  interest." 

"  In  buying  paper  from  a  broker,  we  reckon  on  the  basis  of  360  days,  no  matter  what 
the  rate  of  discount.1' 

"  If  we  buy  notes  absolutely— without  any  recourse  to  the  seller— as  we  frequently  do  of 
note-brokers  and  dealers  in  commercial  paper — the  usage  is  for  banks  to  take,  and  brokers 
to  allow,  interest  for  the  days  to  run  to  maturity  on  the  basis  of  360  days  to  the  year." 

"  In  discounting  notes  we  reckon  interest  on  the  basis  of  365  days  to  the  year,  while  in 
making  '  Call  Loans  '  (357)  the  basis  of  reckoning  ie  360  days." 

"  All  business  with  '  Wall  St.'  on  stock  loans,  whether  on  demand  or  time,  is  calculated 
on  the  basis  of  360  days  to  the  year." 

EXAM  PLES. 

360.  Find  the  date  of  maturity  and  proceeds  of  the  following 
notes : 

(!•) 

$10000.  NEW  YORK,  July  16,  1881. 

Four  months  after  date,  I  promise  to  pay  to  the  order  of  FISK 
&  HATCH,  Ten  Thousand  Dollars,  at  the  First  National  Bank, 
value  received. 

S.  D.  BABCOCK. 

Discounted  July  16,  1881,  at  §%. 

ANALYSIS. — The  note  is  due  4  months  (353,  6)  and  3  days  (days  of  grace, 
353)  after  July  16,  or  Nov.  19.  From  the  day  of  discount  (July  16)  to  the 
day  of  maturity  (Nov.  19)  there  are  126  days. 

The  interest  of  $10000  for  126  days  at  §%,  if  reckoned  on  the  basis  of 
360  days  to  the  year,  is  $210,  and  the  proceeds  are  $10000  less  $210, 
or  $9790. 

The  interest  on  the  basis  of  365  days  to  the  year  would  be  $2.88  less,  or 
$207.12,  and  the  proceeds  would  be  $9792.88. 

If  the  note  was  discounted  Sept.  1,  the  interest  or  discount  would  be 
reckoned  for  79  days  (Sept.  1  to  Nov.  19). 


BANK   DISCOUNT. 


151 


(*•)  ' 

$8000.  BROOKLYN,  N.  Y.,  July  16,  1881. 

Ninety  days  from  date,  I  promise  to  pay  S.  B.  CHITTENDEN, 
or  order,  Eight  Thousand  Dollars,  value  received. 

A.  A.  Low. 

Discounted  Aug.  31,  1881,  at  6%. 

ANALYSIS. — The  note  is  due  93  days  (353,  6)  after  July  16,  or  Oct.  17. 
Compute  the  discount  for  47  days  (Aug.  31  to  Oct.  17)  on  $8000. 

If  the  note  had  been  discounted  July  16,  the  date  of  the  note,  the 
interest  would  have  been  computed  for  93  days,  the  full  time  of  the  note. 

NOTE. — The  results  of  the  following  examples  will  be  given  on  the 
basis  of  both  360  and  365  days  to  the  year. 


No. 

Date  of  Note. 

Time. 

Face. 

Date  of  Discount. 

Rate  of 
Discount 

3 

Jan  24. 

90  days 

$1200 

Jan   24     

6% 

4 

May  18 

3  mo 

$5280 

May  18     

6% 

5 

Aug.  31  

CO  days 

$2560 

Aug.  31  

$% 

6 

June  4 

4  mo 

$3756 

June  4         . 

1% 

7 

Oct  16 

30  days 

$6425 

Oct    16            .    . 

5% 

8 

Mar  13 

6  mo 

$8375 

Mar  13 

51% 

9 

May  29 

3  mo 

$4500 

July  7  

10% 

10 

July  27 

60  days 

$8240 

Sept    2  

6% 

11 

Mar  28 

90  days 

$4324 

Apr  14  

54% 

12 

May  27 

6  mo 

$4885 

Auo-  15. 

8% 

13 

Jan    3 

120  days 

$9000 

Feb  28 

6% 

14 

Sept.  12    

4  mo. 

$5000 

Oct.  14  

7% 

15 

Nov  1     

90  duvs 

$8000 

Nov.  28  

54% 

Eequired  the  proceeds  and  date  of  maturity  of  the  following 
notes  discounted  (360  days  to  the  year)  through  a  broker,  his 
commission  being  \%  of  the  face  of  the  notes. 


No. 

Date  of  Note. 

Time. 

Face. 

Date  of  Discount. 

Rate  of 
Discount 

16 

Feb  21 

4  mo 

S10000 

Feb  21  

4£& 

17 

June  8        . 

4  mo 

$6000 

June  12 

4c\%> 

18 

Jan    10 

4  mo 

$6000 

Jan   10 

41% 

19 

Mar  3      

6  mo. 

$8775 

Apr.  30  

4|% 

20.  What  were  the  proceeds  of  Note  3,  Art.  352,  if  discounted 
Dec.  16,  1881,  at  the  legal  rate  ? 


152  INTEREST. 

21.  Find  the  date  of  maturity  and  proceeds  of  a  note  of  $5000, 
payable  60  days  from  date,  dated  and  discounted  at  a  Philadelphia 
bank,  Aug.  3.     (See  Art.  358.) 

22.  Find  the  date  of  maturity  and  proceeds  of  a  note  of  $3750, 
payable  60  days  from  date,  dated  and  discounted  at  a  Maryland 
bank,  Jan.  31,  1882. 

^  23.  A  broker  discounts  a  note  payable  in  4  months  at  4f%, 
and  charges  \%  brokerage.  This  is  equivalent  to  what  rate  of 
interest  per  annum,  making  no  allowance  for  the  days  of  grace  ? 

2Jf.  A  merchant  can  discount  a  note  at  his  bank  at  6%, 
365  days  to  the  year,  or  through  n  broker  at  4f  %,  360  days  to  the 
year,  broker's  commission  %%.  How  much  better  is  the  latter 
method  on  a  note  of  $10000,  payable  in  4  months,  dated  and 
discounted  May  21  ? 

Find  the  date  of  maturity  and  proceeds  of  the  following 
interest-bearing  notes  : 

(25.) 
$3000.  ALBANY,  N.  Y.,  September  16,  1881. 

Four  months  after  date,  I  promise  to  pay  W.  J.  KLINE  or 
order,  Three  Thousand  Dollars,  with  interest  at  5$,  value 
received. 

J.  M.  THOMAS. 
Discounted  Nov.  3,  1881,  at  6$. 

NOTE.  —  Compute  the  discount  at  6%  for  77  days  (Nov.  3  to  Jan.  19)  on 
the  amount  due  at  maturity  ($3000  plus  the  interest  of  $3000  for  4  months 
and  3  days  at 


26.  A  note  dated  May  27,  1879,  payable  in  3  months,  for  $3750, 
with  interest  at  7%  ;  discounted  May  27,  1879,  at  8$. 

27.  A  note  dated  Jan.   16,    1879,   payable  in  4  months,  for 
$1632,  with  interest  at  Q%  ;  discounted  Mar.  5,  1879,  at  1%. 

28.  A  note  dated  Oct.  12,  1878,  payable  in  6  months,  for  $875, 
with  interest  at  1%;  discounted  Jan.  10,  1879,  at  10$. 

29.  For  what  amount  must  a  note  be  given  for  60  days  to 
afford  $1000  proceeds,  if  discounted  at  6$  ? 

ANALYSIS.  —  The  proceeds  of  any  note  is  as  many  times  greater  than  the 
proceeds  of  $1,  as  the  face  of  the  note  is  greater  than  $1.  If  a  note  of  $1  is 
discounted  for  63  days,  at  6%,  it  will  afford  $.9895  proceeds  ;  to  afford  $1000 
proceeds,  the  face  of  the  note  must  be  as  many  times  $1,  as  $.9895  is  con- 
tained times  in  $1000,  or  $1010.61. 


PARTIAL    PAYMENTS.  153 

The  following  approximate  method  is  generally  used  by  business  men  : 
To  the  given  proceeds,  add  the  interest  for  the  given  time. 

The  interest  of  $1000  for  63  days  is  $10.50.  $1000  +  $10.50  -  $1010.50. 
Since  the  interest  is  reckoned  on  the  proceeds  instead  of  the  face  of  the  note, 
the  error,  11  cents,  is  equivalent  to  the  interest  of  the  interest  ($10.50)  for  the 
given  time. 

Where  greater  accuracy  is  required,  the  necessary  correction  may  be 
made.  The  interest  of  $10.50  for  63  days  is  11  cents.  $1010.50  +  $.11 
=  $1010.61. 

30.  A  owes  B  $1500  ;  how  large  a  90-day  note  must  A  give  B 
that  when  discounted  at  a  bank  at  §%,  the  proceeds  will  be  suffi- 
cient to  pay  the  debt  ? 

81.  I  hold  a  note  of  $3000  against  Mr.  C.,  which  he  pays  by 
giving  a  new  note  at  90  days  for  $1500,  and  the  balance,  includ- 
ing the  discount  on  the  new  note,  in  cash.     Required  the  amount 
of  cash  paid.  ^ 

82.  A  merchant  having  $8000  to  pay,  gets  a  note  for  $500Q> 
that  will  mature  in  40  days,  discounted  at  a  bank  at  6%.     How 
large  a  note  must  he  draw,  payable  in  90  days,  for  discount  at 
the  same  rate,  that  the  proceeds  of  the  two  notes  may  enable  him 
to  meet  his  payment  ? 

PARTIAL     PAYMENTS. 

361.  Partial  Payments  are  payments  in  part  of  a  note, 
mortgage,  or  other  debt,  made  at  different  times. 

362.  Indorsements  are  the  acknowledgments  of  the  pay- 
ments, written  on  the  back  of  the  note,  mortgage,  etc.,  and  stating 
the  amount  and  date  of  the  payment. 

Special  receipts  are  sometimes  given  for  such  payments. 

UNITED     STATES     RULE. 

363.  Ex.     How  much  would  be  due  Sept.  1, 1882,  on  a  note 
of  $600,  dated  March  1,   1882,  with  interest  at  6^?     Suppose  a 
payment  of  $100  be  made  Sept.  1,  1882,  to  pay  the  interest  and 
part  of  the  principal,  how  much  would  then  be  due  ?  Ans.  $518. 

Ex.  How  much  would  be  required  to  settle  the  above  note 
Jan.  1,  1883,  the  balance  of  $518  remaining  on  interest  at  the 
same  rate  from  Sept.  1,  1882?  Ans.  $528.36. 


154  INTEREST. 

Ex.  Find  the  amount  due  on  the  following  note,  Jan.  19, 
1885: 

$1000.  BOSTON,  MASS.,  Aug.  1,  1881. 

One  year  after  date,  I  promise  to  pay  JOKDAN,  MARSH  &  Co., 
or  order,  One  Thousand  Dollars,  for  value  received,  with  interest 
from  date,  at  6  per  cent. 

ALEXANDER  H.  RICE. 

On  this  note  are  the  following  indorsements : 
Received  Apr.  21,  1882,  $200.  Received  Aug.  1,  1883,  $100. 

Received  Dec.  1,  1882,  $25.  Received  July  7,  1884,  $400. 

NOTE. — The  method  given  in  the  following  operation,  is  that  adopted  by 
the  Supreme  Court  of  the  United  States,  and  has  been  made  the  legal  method 
of  nearly  all  the  States.  By  the  United  States  Rule,  as  this  is  generally 
called,  settlements  are  made  whenever  the  payments  are  equal  to  or  exceed 
the  interest  due ;  if  the  payment  exceeds  the  interest,  it  is  applied  first  to 
discharge  the  interest,  and  the  surplus  is  applied  towards  paying  the  princi- 
pal ;  if  the  payment  is  less  than  the  interest,  it  is  not  applied  until  the 
payments,  taken  together,  are  sufficient  to  pay  all  interest  due  ;  since  no 
unpaid  interest  is  added  to  the  principal  to  draw  interest,  a  new  principal  can 
never  be  greater  than  the  preceding  principal. 

OPERATION. 

Face  of  note,  or  principal,  from  Aug.  1, 1881        ....        $1000 
Interest  from  Aug.  1,  1881,  to  Apr.  21,  1882  (8  mo.  20  da.),  added  43.33 

Amount,  Apr.  21,  1882, 1043.33 

First  payment,  Apr.  21,  1882, 200.00 

New  principal  from  Apr.  21,  1882 843.33 

Interest  of  $843.33  from  Apr.  21,  1882,  to  Dec.  1,  1882, 

(Vmo.lQda.) $30.92 

(Interest  exceeds  the  payment,  and  a  new  principal  is 

not  formed.) 
Interest  of  $843.33  from  Dec.  1,  1882,  to  Aug.  1,  1883, 

(8  mo.) 33.73  _6465* 

[Payments  $125  ($25  +  $100),  now  greater  than  the  interest  due 

($64.65)]. 

Amount,  Aug.  1,  1883, 907.98 

Second  and  third  payments,  $25  +  $100 125 

New  principal  from  Aug.  1,  1883 782.98 


*  In  many  cases  it  can  be  determined  mentally  in  advance  whether  the  payment  is 
greater  or  less  than  the  interest.  In  this  case  the  interest  could  he  taken  at  once  from 
Apr.  21, 1882,  to  Aug.  1, 1833  (1  yr.  3  mo.  10  da.),  since  it  is  evident  that  the  payment  ($25)  is 
less  than  the  interest  of  $843.33  for  7  mo.  10  da.  (The  interest  of  $800  for  7  mo.  is  3J-  x  $8,  or 
$28,  and  it  would  be  more  on  $843.33  for  7  mo.  10  da.)  If  it  is  doubtful  whether  the  payment 
is  greater  or  less  than  the  interest,  perform  all  the  work. 


PARTIAL    PAYMENTS.  155 

New  principal  from  Aug.  1,  1883 $782.98 

Interest  of  $782. 98  from  Aug.  1 , 1883,  to  July  7, 1884  (1 1  mo.  6  da. )  43.85 

Amount,  July  7,  1884, 826.83 

Fourth  payment,  July  7,  1884, 400 

New  principal  from  July  7,  1884 426.83 

Interest  of  $426.83  from  July  7,  1884,  to  Jan.  19,  1885  (6  mo. 

12  da.) 13.66 

Amount  due  Jan.  19,  1885,  the  final  day  of  settlement,          .        Ana.  $440.49 

364.  UNITED   STATES  RULE. — Find  the  amount    of  the 
given  principal  to  the  time  when  the  payment  or  the  sum 
of  the  payments  exceeds  the  interest  due;  subtract  from 
this  amount  the  payment  or  the  sum  of  the  payments. 
Treat  the  remainder  as  a  new  principal,  and  proceed  as 
before,  to  the  time  of  settlement. 

EXAMPLES. 

365.  NOTES. — 1.  In  the  following  examples,  find  the  time  by  compound 
subtraction. 

2.  In  the  first  five  examples,  all  the  payments  exceed  the  interest. 

91680.  TBENTOJ*,  N.  J.,  Oct.  9,  1880. 

1.  On  demand,  I  promise  to  pay  COOPER,  HEWITT  &  Co.,  or 
order,  Sixteen  Hundred  Eighty  Dollars.     Value  received. 

A. 


On  this  note  were  indorsed  the  following  payments  : 
Dec.  21,  1881,  received  $289.12.      June  9,  1883,  received  $991.50. 
How  much  was  due  Jan.  30,  1884  ? 

2.  On  a  note  dated  May  11,  1877,  for  $2000,  are  the  following 
indorsements  :— Aug.   6,  1879,  $361;   Feb.  11,  1880,   $901.60; 
Nov.  2,  1882,  $1000.     What  remained  due  Feb.  2,  1883,  at  6$? 

A  4-    Kf/  V 

£    ja.i  dye  . 

3.  On  a  note  dated  July  11,  1878,  for  $2400,  are  the  following 
\  indorsements  :  — Sept.  17,  1879,  $200  ;  Jan.  29, 1880,  $400  ;  Nov. 

29,  1881,  $1150.     What  is  the  amount  due  Jan.  11,  1882,  the 
interest  being  at  6%  ?    At  1%  ? 

4.  On  a  mortgage  for  $1700,  dated  May  28,  1880,  there  was 
paid  Nov.  12,  1880,  $80;   Sept.   20,  1881, '$314;   Jan.  2,  1882, 
$50  ;  Apr.  17,  1882,  $160.     What  was  due  Dec.  12,  1882,  at  6$? 
At  8^? 


156  INTEREST. 

5.  On  a  note  dated  May  30,  1879,  for  $1666,  are  the  following 
indorsements  :  — Apr.  9,  1880,  $314;   Nov.  4,  1880,  $180;   Aug. 
25,  1881,  $575.     What  was  due  June  30,  1882,  at  Q%  ?    At  S%? 

6.  What  was  the  amount  due  Oct.  17,  1881,  upon  a  note  for 
$1000,  dated  New  York,  Mar.  2,  1880,  and  on  which  the  following 
payments  were  indorsed :  — June  2,  1880,  $80;    Dec.  15,  1880, 
$20  ;  May  2,  1881,  $32;  June  2,  1881,  $60? 

7.  A  note  for  $3600,  dated  May  12,  1880,  bore  the  following 
indorsements  :  — Jan.  2,  1881,  $255  ;  Mar.  15,  1881,  $225;  June 
3,  1881,  $120  ;  Aug.  6,  1881,  $300  ;  Feb.  3, 1882,  $30.     What  was 
due  June  2,  1882,  at  6%  ?    At  10^  ? 

8.  A  note  for  $4000,  dated  Mar.  9,  1874,  was  indorsed  as  fol- 
lows :  — Jan.  18,  1876,  $300  ;  June  4,  1876,  $400;  Dec.  9,  1876, 
$1800  ;  Sept.  1,  1879,  $2000.     How  much  had  to  be  paid  Jan.  1, 
1880,  to  take  up  the  note,  at  §%  ?    At  1%  ? 

9.  A  mortgage  of  $6000  is  dated  May  9,  1877,  on  which  there 
were  the  following  payments:  —  July  15,  1878,  $500;  Nov.  27, 
1878,  $1000;  June  1,  1879,  $100;  May  9,  1880,  $275;  Sept.   27, 

1880,  $2000.     What  was  due  Nov.  9,  1880,  the  interest  being  at 
Q%?    At  12^? 

10.  What  remained  due  June  3,  1882,  on  a  note  dated  June 
21,  1880,  for  $3300  with  interest  at  the  legal  rate  in  Illinois,  the 
following  payments  having  been  made  ?    Oct.  9,  1880,  $90  ;  Jan. 
15,  188.1,  $60 ;  Mar.  27,  1881,  $100 ;  Aug.  6,  1881,  $60  ;  Dec.  15, 

1881,  $500.     WThat  remained  due  at  the  legal  rate  in  Nevada  ? 

MERCANTILE   RULES. 

366.  The  following  methods  are  frequently  used  by  merchants 
in  finding  the  balance  due  on  a  note  where  partial  payments  have 
been  made.     They  are  similar  to  the  methods  in  general  use  for 
finding  the  balance  due  on  an  open  account  (451). 

367.  When  the  note  runs  for  one  year  only,  or  less. 

368.  RULE. — Compute  the  interest  on  the  principal  from 
the  time  it  commenced  to  draw  interest,  and  on  each  pay- 
ment from  the  time  it  was  made  until  the  time  of  settle- 
ment, and  deduct  the  amount  of 'all  the  payments,  includ- 
ing interest,  from  the  amount  of  the  principal  and  interest. 


PARTIAL    PAYMENTS.  157 

NOTES. — 1.  This  rule  is  used  by  some  merchants  when  the  note  runs 
more  than  one  year,  although  it  is  greatly  to  the  disadvantage  of  the  creditor, 
or  holder  of  the  note. 

2.  In  solving  examples  by  this  rule,  the  different  methods  for  finding 
time  and  interest,  given  in  Art.  299,  are  used.  The  results  of  the  following 
examples  will  be  given  for  the  first  method  (Compound  Subtraction  and 
360  days  to  the  year). 

EXAMPLES. 

369.  1.  According  to  the  mercantile  rule,  find  the  balance 
due  May  12,  1882,  on  a  note  for  $2400,  dated  July  12,  1881,  on 
which  the  following  payments  have  been  made  :  Dec.  16,  1881, 
$40;  Jan.  2,  1882,  $100;  Mar.  15,  1882,  $150. 

OPERATION. 

Face  of  note,  or  principal,  July  12,  1881, $24QO.OO 

Interest  on  the  same  to  May  12,  1882  (10  mo,}         ....          120.00 

Amount,  May  12,  1882 2520.00 

First  payment,  Dec.  16,  1881, $40.00 

Interest  on  the  same  to  May  12,  1882  (4  7720.  26  da.)        .  .97 

Second  payment,  Jan.  2,  1882, 100.00 

Interest  on  the  same  to  May  12,  1882  (4  mo.  10  da.}        .  2.17 

Third  payment,  Mar.  15,  1882, 150.00 

Interest  on  the  same  to  May  12, 1882  (1  mo.  27  da.)        .          1.42          294.56 
Balance  due  May  12,  1882 $2225.44 

2.  On  a  note  dated  Jan.  13,  1882,  for  $1234,  are  the  following 
indorsements:  May  17,  1882,  $234;  June  16,  1882,  $345;  July 27, 
1882,  $123  ;  Sept.  19,  1882,  $135.     What  remained  due  Nov.  13, 

1882,  at  6%  ?    At  1%  ? 

3.  A  note  for  $1567,  dated  Jan.  14,  1881,  bore  the  following 
indorsements :  Mar.  11,  1881,  $50  ;  May  13,  1881,  $245 ;  June  19, 
1881,  $374;  Aug.  30,  1881,  $412  ;  Sept.  28,  1881,  $316.40.   What 
was  due  Jan.  1,  1882,  at  6%?     At  5%? 

4.  On  a  note  dated  Aug.  17,  1881,  for  $3300,  were  the  follow- 
ing indorsements :  —  Dec.   18,  1881,  $320  ;   Feb.  5,  1882,  $425  ; 
Apr.  13,  1882,  $550;  June  29,  1882,  $630  ;  July  16,  1882,  $375  ; 
Aug.  1,  1882,  $500.      What  amount  was  due  Aug.  17,  1882,  at 
6%  ?     At  10$  ? 

5.  On  a  note  dated  Mar.  16,  1883,  for  $2468,  are  the  following 
indorsements  :  July  11,  1883,  $750 ;  Aug.  4,  1883,  $428 ;  Sept.  21, 

1883,  $150;  Nov.  12,  1883,  $170  ;   Dec.  18,  1883,  $128  ;   Jan.  16, 

1884,  $224 ;    Feb.    13,    1884,    $600.     What  is  the  amount  due 
Mar.  6,  1884,  at  6^  ?    At 


158  INTEREST. 

370.  When  the  note  runs  for  more  than  one  year. 

371.  Since   it   is   the   custom  of  merchants  and  bankers  to 
balance  their  accounts  annually,  the  following  method  is  used  by 
them  in  computing  the  balance  due  on  a  note  when  it  runs  more 
than  one  year. 

It  is  equivalent  to  finding  the  balance  due  yearly  by  the  previous  rule,  and 
treating  the  balance  as  a  new  principal.  The  periodical  settlements  are  made 
annually,  semi-annually,  or  quarterly,  depending  upon  the  custom  of  the 
merchant  or  banker  in  balancing  his  accounts.  Some  merchants  make  the 
end  of  the  business  year,  Jan.  1  or  July  1,  the  periodical  rest,  or  date  of 
settlement  for  notes  and  accounts. 

When  payments  are  made  yearly  greater  than  the  interest  due,  this  rule 
is  the  same  as  the  New  Hampshire  rule  for  notes  "  with  interest  annually." 

372.  RULE. — Find  the  amount  of  the  principal  for  one 
year ;  also  of  each  payment  made  during  the  year  from  the 
time  the  payment  ivas  made  to  the  end  of  the  year  ( 1  yr. 
from  the  date  of  the  note).    From  the  amount  of  the  prin- 
cipal, subtract  the  sum  of  the  payments,  including  interest. 
With  the  remainder  as  a  new  principal,  proceed  thus  for 
each  entire  year  that  follows,  and  for  the  interval  between 
the  end  of  the  last  year  and  the  final  date  of  settlement. 

EXAM  PLES. 

373.  1.   By  the  above  rule,  find  the  balance  due  Jan.  19, 1885, 
at  6%,  on  a  note  for  $2400  dated  Aug.  1,  1881,  on  which  the  fol- 
lowing payments  have  been  made  :  —  Apr.  21,  1882,  $200;  Dec.  1-, 
1882,  $25;  Aug.  1,  1883,  $100;  July  7,  1884,  $400.     (Time  by 
Compound  Subtraction.) 

OPERATION. 

Face  of  note,  or  principal,  Aug.  1,  1881, $2400.00 

Interest  on  the  same  for  1  year, 144.00 

Amount,  Aug.  1,  1882, 2544.00 

First  payment,  Apr.  21,  1882, $200.00 

Interest  on  the  same  to  Aug.  1,  1882  (3  mo.  10  da.}        .           3.33  203.33 

Balance  and  new  principal,  Aug.  1,  1882,                 ....  2340.67 

Interest  on  the  same  for  1  year, 140.44 

Amount,  Aug.  1,  1883, 2481.11 


PARTIAL    PAYMENTS.  159 

Amount,  Aug.  1,  1883, 2481.11 

Second  payment,  Dec.  1,  1882, $25.00 

Interest  on  the  same  to  Aug.  1,  1883  (8  mo)  .        .        .  1.00 

Third  payment,  Aug.  1,  1883, 100.00  126.00 

Balance  and  new  principal,  Aug.  1,  1888, 2355.11 

Interest  on  the  same  for  1  year, 141.31 

Amount,  Aug.  1,  1884, 2490.42 

Fourth  payment,  July  7,  1884, $400.00 

Interest  on  the  same  to  Aug.  1,  1884  (24  da.)          .        .           1.60  401.60 

Balance  and  new  principal,  Aug.  1,  1884, 2094.82 

Interest  on  the  same  to  date  of  settlement,  Jan.  1 9, 1885  (5  mo.  18  da.)  58.65 

Balance  due  Jan.  19,  1885, $2153.47 

i          2-10.    Solve    Examples    2-10,  Art.   365,   according  to  the 
mercantile  rule. 

CONNECTICUT     RULE. 

374.  The  following  rule  for  computing  interest  on  obliga- 
tions, where  one  or  more  payments  have  been  made,  was  estab- 
lished   by   the   Superior   Court    of    Connecticut,    March,    1784. 
(Kirby's  Eeports,  page  49.) 

375.  EULE. — /.  Compute  the  interest  to  the  time  of  the 
first  payment ;  if  that  be  one  year,  or  more,  from  the  time 
the  interest  coimnenced,  add  it  to  the  principal,  and  deduct 
the  payment  from  the  sum  total.     If  there  be  after-pay- 
ments made,  compute  the  interest  on  the  balance  due  to  the 
next  payment,  and  then  deduct  the  payment  as  above ;  and 
in  lilce  manner  from  one  payment  to  another,  till  all  the 
payments  are  absorbed ;  provided  the  time  between  one  pay- 
ment and  another  be  one  year  or  more. 

II.  But   if   any  payment    ~be   made  before  one  year's 
interest  hath  accrued,  then   compute  the  interest  on  the 
principal  sum  due  on  the  obligation  for  one  year,  add  it  to 
the  principal,  and  compute  the  interest  on  the  sum  paid, 
from  the  time  it  was  paid,  up  to  the  end  of  the  year ;   add 
it  to  the  sum  paid,  and  deduct  that  sum  from  the  principal 
and  interest  added  as  above. 

III.  If  any  payment  be  made  of  a  less  sum  than  the 
interest  arisen  at   the  time  of  such  payment,  no   interest 


160 


INTEREST. 


is  to  be  computed,  but  only  on  the  principal  sum  for  any 
period. 

NOTES. — 1.  Should  the  final  date  of  settlement  be  less  than  one  year 
from  the  last  date  of  settlement,  compute  the  interest  on  the  principal  and 
the  payments,  if  any,  to  the  final  date  of  settlement. 

2.  When  the  time  between  the  payments  is  one  year  or  more,  and  the 
payments  exceed  the  interest  due,  the  Connecticut  Rule  is  the  same  as  the 
U.  S.  Rule  (364).  When  the  time  between  the  payments  is  less  than  one 
year,  and  the  payment  exceeds  the  interest  due  at  its  date,  the  settlement  ia 
made  by  the  first  Mercantile  Rule  (368). 


EXAMPLES. 

376.  1.  According  to  the  law  of  Connecticut,  how  much  is 
due  June  1,  1885,  on  a  note  dated  Aug.  1,  1881,  for  $1000,  the 
following  payments  having  been  made?  Apr.  21,  1882,  $100; 
Dec.  1,  1883,  $300;  July  1,  1884,  $20;  Sept.  1,  1884,  $200; 
Mar.  1,  1885,  $300. 


OPERATION. 

Face  of  note,  or  principal, 

Interest  on  the  same  for  1  year,          .... 

Amount,  Aug.  1,  1882, 

First  payment,  Apr.  21,  1882, 

Interest  on  the  same  to  Aug.  1,  1882  (3  mo.  10  da.} 

Balance  and  new  principal,  Aug.  1,  1882, 

Interest  to  date  of  next  payment,  Dec.  1,  1883  (1  yr.  4  mo.} 

Amount,  Dec.  1,  1883 

Second  payment,  Dec.  1,  1823, 

Balance  and  new  principal,  Dec.  1,  1883,  .... 

Interest  on  the  same  for  1  year, 

Amount,  Dec.  1,  1884, 

Third  payment,  July  1,  1884  (less  than  interest  due) 

Fourth  payment,  Sept.  1,  1884, 

Interest  on  the  same  to  Dec.  1, 1884  (3  mo.} 

Balance  and  new  principal,  Dec.  1,  1884,  .... 

Interest  to  final  date  of  settlement,  June  1,  1885  (6  mo.} 

Amount  June  1,  1885, 

Fifth  payment,  Mar.  1,  1885, 

Interest  on  same  to  June  1,  1885  (3  mo.}  . 
Balance  due  at  date  of  settlement,  June  1,  1885, 


$100.00 
1.67 


$20.00 

200.00 

3.00 


$300.00 
4.50 


$1000.00 
JSO^OO 
1060.00 

101.67 
958.33 

_76i67 
1035.00 
300.00 
735.00 
J14.10 
779.10 


223.00 

556.10 

16.68 

572.78 

304.50 

268.28 


2-10.  Solve  Examples  2-10,  Art.  365,  according  to  the  Con- 
necticut Eule,  at  the  legal  rate  (298). 


PARTIAL    PAYMENTS.  161 

NEW     HAMPSHIRE     RULE.* 

377.  According  to  the  laws  of  New  Hampshire,  when  pay- 
ments are  made    upon  a  note,  or  other  contract,  by  virtue  of 
which  interest  is  payable  annually  (336),  they  should  be  applied 
in  the  following  order  to  the  payment  of — 

1.  Any   simple    interest    that   may   have   accrued   upon   the 
annual  interest. 

2.  The  annual  interest.  3.  The  principal. 

378.  EULE. — Find  the  interest  due  upon  the  principal 
and  the  annual  interest  at  the  annual  rest  (the  time  when 
the  annual  interest  becomes  due  from  year  to  year)  next 
after  the  first  payment.      To   the  payment   or  payments 
made  before  this  rest,  add  interest  from  the  dates  when 
they  were  inade  to  the  date  of  the  rest,  unless  there  is  no 
interest  due  upon  the  principal,  excepting  that  which  is 
accruing  during  the  year  in  whicli  the  payment  or  pay- 
ments were  made,  and  the  payments  together  are  less  than 
the  interest  thus  accruing,  in  which  last  case  no  interest  is 
to  be   added  to  the  payments.      Deduct  the   payment  or 
payments,   with  or  ivithout   interest,   as    aforesaid,   from 
the    amount    of   principal,   annual    interest,   and  simple 
interest  upon    the    annual  interest   due    at   the   time  of 
said  rest,  if  such  payment  or  payments  equal  or  exceed 
the  annual  and  simple  interest  then  due ;  if  less  than  such 
annual  and  simple  interest,  but  greater  than  the  simple 
interest  due  upon  the   annual  interest,  deduct  the  same 
from  the  sum  of  the  annual  and  simple  interest,  and  upon 
the  balance  of  such  annual  interest  find  simple  interest  to 
the  time  ivhen  the  next  payment  or  payments  are  applied  ; 
if  less  than  the  simple  interest   due    upon    the    annual 
interest,  deduct  the  same  from  such  simple  interest  and 
add  the  balance  ivithout  interest  to  the  other  interest  due 
at  the  time  luhen  the  next  payment    or    payments    are 
applied. 

Proceed  in  like  manner  to  the  time  of  the  first  annual 
rest  following  the  next  payment,  and  to  the  end  of  the  time 
required. 

*  From  Report  of  State  Superintendent  of  Public  Instruction  (1877). 
11 


162 


INTERE  ST. 


EXAMPLES. 

379.  1.  According  to  the  law  of  New  Hampshire,  how  much 
is  due  Jan.  1,  1886,  on  a  note  dated  Jan.  1,  1880,  for  $2000,  with 
interest  annually  at  6%,  the  following  payments  having  been 
made :  July  1,  1882,  $500 ;  Oct.  1,  1883,  $50. 

OPERATION. 

First  annual  interest  due  Jan.  1,  1881,  $120  +  2  yr.  simple  interest 
thereon,  $14.40 

Second  annual  interest  due  Jan.  1, 1882,  $120  + 1  yr.  simple  interest 
thereon,  $7.20 • 

Third  annual  interest  due  Jan.  1,  1883, 

Principal 


$134.40 

127.20 
120.00 
2000.00 

$2381.60 


$500 
15 


First  payment,  July  1,  1882,      .... 
Interest  thereon  from  July  1,  1882,  to  Jan.  1,  1883, 

Balance  of  principal  due  Jan.  1,  1883, 

Fourth  annual  interest  of  $1866.60,  due  Jan.  1,  1884, 
Second  payment,  Oct.  1,  1883  (being  less  than  the  interest  accruing 
during  the  year,  it  does  not  draw  interest)    .... 

Balance  of  fourth  annual  interest  unpaid 

Fifth  annual  interest  of  $1866.60,  due  Jan.  1,  1885, 

Sixth  annual  interest  of  $1866.60,  due  Jan.  1,  1886, 

Simple  interest  on  unpaid  balance  of  fourth  annual  int.  for  2  yr.  . 

Simple  interest  on  fifth  annual  interest  for  1  year   .... 

Balance  of  principal 

Amount  due  Jan.  1, 


515.00 

1866.60 

112.00 


50.00 
62.00 
112 
112 
7.44 
6.72 
1&J8.60 
2166.76 

2-10.  Solve  Examples  2-10,  Art.  365,  according  to  the  New 
Hampshire  Rule,  at  the  legal  rate  (298),  supposing  each  note  to 
contain  the  words  "  with  interest  annually." 

VERMONT   RULE. 

38O,  The  Vermont  Rule  for  notes  with  interest  is  essentially 
the  same  as  the  United  States  Rule  (364) ;  and  for  notes  "  with 
interest  annually,"  it  is  the  same  as  the  New  Hampshire  Rule, 
except  that  when  payments  -are  made  on  account  of  interest  accru- 
ing but  not  yet  due,  they  draw  interest  from  the  date  they  were 
made  to  the  annual  rest,  whether  they  are  greater  or  not  than  the 
interest  accruing  during  the  year. 

Thus,  by  the  Vermont  Rule,  the  payment  of  $50,  in  the  above  example, 
would  draw  interest  from  Oct.  1,  1883  to  Jan.  1,  1884,  or  3  months.  The 
unpaid  balance  of  fourth  annual  interest  would  be  $61.25  ($112  —  $50.75). 


RATIO     AND     PROPORTION. 


D  EFINITION  S. 

381.  Ratio  is  the  relation  of  two  numbers  as  expressed  by  the 
quotient  of  the  first  divided  by  the  second.    Thus  the  ratio  of  6  to  3 
is  6-r-S,  or  2. 

1.  There  is  no  ratio  between  quantities  of  different  kinds  ;  as  6  bu.  and 
3/£.     But  a  ratio  exists  between  quantities  of  the  same  kind  though  of  differ- 
ent denominations ;  as  6  ft.  and  8  in.     To  express  the  ratio  in  such  cases,  the 
quantities  must  first  be  reduced  to  the  same  denomination.     Thus,  the  ratio 
of  6  ft  to  8  in.  is  72  in.-r-S  in.,  or  9. 

2.  The  ratio  between  two  numbers  is  denoted  by  placing  a  colon  (the  sign 
of  division  without  the  horizontal  line)  between  them.     Thus,  the  ratio  of 
G  to  3  is  expressed  6  :  3. 

382.  The  numbers  whose  ratio  is  expressed  are  the  terms  of 
the  ratio.     The  two  terms  of  a  ratio  form  a  couplet,  the  first  of 
which  is  the  antecedent,  and  the  second,  the  consequent. 

383.  Proportion  is  an  equality  of  ratios. 

The  ratio  of  6  yd.  to  3  yd.  is  2,  and  the  ratio  of  $24  to  $12  is  2  ;  hence 
from  the  two  equal  ratios  the  following  proportion  can  be  formed — 6  yd. :  3  yd. 
—  $24  :  $12.  This  expression  is  read,  "  The  ratio  of  6  yd.  to  3  yd.  equals  the 
ratio  of  $24  to  $12."  In  place  of  the  sign  of  equality  (=),  four  dots  (: :)  are 
generally  used  ;  thus,  6  yd. :  3  yd.  : :  $24  :  $12.  The  expression  is  also  read, 
"6yd.  is  to  3  yd.  as  $24  is  to  $12." 

384.  The  first  and  fourth  terms  of  a  proportion  are  called  the 
extremes  ;  and  the  second  and  third,  the  means. 

385.  PRINCIPLES. — 1.  Tlie  product  of  the  means  is  equal  to 
the  product  of  the  extremes. 

2.  A  missing  mean  may  be  found  by  dividing  the  product  of 
tlie  extremes  by  the  given  mean. 


164  RATIO    AND    PROPORTION. 

3.  A  missing  extreme  may  be  found  by  dividing  the  product  of 
the  means  by  the  given  extreme. 

386.  To  solve  examples  by  proportion. 

Ex.     If  24  hats  cost  $27,  what  will  32  hats  cost  ? 

ANALYSIS. — For  convenience,  make  the  fourth  term  the  missing  term, 
or  the  required  answer.  Since  the  third  and  fourth  terms  must  be  of  the 
same  denomination  and  the  denomination  of  the  answer  will  be  dollars,  take 
$27  as  the  third  term.  From  the  nature  of  the  example,  the  answer  will  be 
more  than  $27,  the  third  term,  therefore  make  32  hats  the  second  term,  and 
24  hats  the  first  term.  The  proportion  will  then  be  stated  as  follows  : 
24  hats  :  32  hats  : :  $27  :  x  (Let  x  represent  the  unknown  term).  Multiplying 
32  by  27,  and  dividing  the  product  by  24,  the  fourth  or  missing  term  will  be 
$36. 

387.  RULE. — For  convenience,,  take  for  the  third   term 
the  number  that  may  form  a  ratio  with,  or  is  of  the  same 
denomination  as,   the   answer.       If  from  the  nature  of  the 
example,  the  answer  is  to  be  greater  than  the  third  term, 
make  the  greater  of  the  two  remaining  terms  (which  must 
be  of  the  same  denomination)  the  second  term ;  when  not, 
make  the  smaller  the  second   term.     Then  multiply  the 
means  (the  second  and  third)  together,  and  divide  their 
product  by  the  given  extreme  (the  first  term). 

NOTE. — After  the  example  is  stated,  any  factor  of  the  given  extreme  may 
be  cancelled  with  an  equal  factor  of  either  of  the  means. 

EXAMPLES. 

388.  Find  the  missing  term  (represented  by  x)  in  each  of  the 
following  proportions  (See  Principles,  Art.  385) : 

1.  16  :  x  ::  24 : 18.  5.  $48  :  $75  : :  $32  :  x. 

2.  x :  27  :  :  18  :  54.  6.  $375  :  $144  :  :  625  Ib. :  x. 

3.  32  :  27  : :  x  :  135.  7.  $1728  :  $288  : :  $666  :  x. 

4.  24  bu. :  32  bu.  : :  $27  :  x.      8.  144  yd.  :  175  yd.  :  :  $18  :  x. 
9.  If  19  yd.  of  silk  cost  $28.50,  what  will  37  yd.  cost? 

10.  If  64  yd.  of  carpet  36  in.  wide  will  cover  a  floor,  how  many 
yards  27  in.  wide  will  be  required  to  cover  the  same  floor  ? 

11.  A  cane  3ft.  3  in.  high  casts  a  shadow  tyft.  long;  how 
long  a  shadow  is  cast  by  the  steeple  of  a  church  which  is  234  feet 
high? 


RATIO    AND    PROPORTION.  165 

12.  If  the  freight  of  a  long  ton  (172,  3)  is  70  shillings,  what  is 
the  freight  of  16375  pounds? 

13.  The  net  assets  of  a  bankrupt  are  $27675,  and  the  liabilities 
$138375.     How  much  must  be  paid  to   Mr.  A,  whom  he  owes 
$4800? 

14.  A  building  is  insured  in  several  companies  for  $28000. 
During  a  fire  the  building  is  damaged  to  the  amount  of  $13500. 
What  is  the  loss  of  company  A,  whose  risk  is  $5000  ? 

15.  A  invests  in  business  $8450,  and  B  $7200,  and  the  gain  or 
loss  is  divided  according  to  the  investments.     What  is  each  part- 
ner's share  of  gain,  the  total  gain  being  $3474.30? 

16.  The  U.  S.  gold  dollar  (181,  183)  contains  23.22  (25.8 
— A)  grains  of  pure  gold,  and  the  standard  silver  dollar  371.25 
(412.5— iV )  grains  of  pure  silver.     What  is  the  relative  value  of 
pure  gold  to  pure  silver  ? 

17.  The  assessed  value  of  the  property  of  a  certain  town  is 
$325000,  and  the  total  tax  is  $10238.    How  much  is  the  tax  of 
Mr.  A,  whose  property  is  valued  at  $5700  ? 

18.  A  bankrupt  whose  assets  were  $43225,  pays  44  cents  on 
a  dollar ;  what  did  his  debts  amount  to  ? 

19.  A  cask  holds  45  English  (167)  gallons  ;  how  many  Amer- 
ican gallons  will  it  hold  ? 

20.  A  company  with  a  capital  of  $250000  divides  $8750  among 
its  stockholders.     How  much  will  be  received  by  a  stockholder 
who  owns  36  100-dollar  shares? 

21.  If  a  long  ton  of  coal  is  worth  $4.25,  what  is  the  value  of  a 
short  ton  ? 

22.  If  a  farm  valued  at  $4500  is  taxed  $26.24,  what  should  be 
the  tax  on  property  valued  at  $23500  ? 

23.  If  a  man  can  walk  a  mile  in  10  minutes,  in  what  time 
can  he  walk  a  kilometer  ? 

24.  A  piece  of  land  40  rods  long  and  4  rods  wide  contains  an 
acre  ;  what  is  the  breadth  of  a  piece  32  rods  long,  that  is  equiva- 
lent to  an  acre  ? 

25.  A  merchant  gains  $625  by  selling  $12000  worth  of  goods  ; 
what  amount  must  he  sell  to  gain  $8000  ? 

26.  Find  the  value  of  6  T.  (2240  lb.)  7  cwt.  2  qr.  20  Ib.  of  iron 
at  85s.  per  ton. 

27.  How  many  feet  of  boards  will  be  required  for  a  fence 
764  feet  long,  if  888  feet  of  boards  are  required  for  288  feet  ? 


INSURANCE. 


DEFINITIONS. 

389.  Insurance  is  a  contract  by  which  one  party   (The 
Insurer   or  Underwriter)  engages  for  a  stipulated  consideration 
(The  Premium)  to  make  up  a  loss  which  another  may  sustain. 

Insurance  is  effected  on  property  against  loss  or  damage  by 
fire  and  water,  and  on  lives  of  persons.  (For  Life  Insurance,  see 
Art.  524:.) 

Insurance  is  also  effected  against  accidents  to  persons,  the  breakage  of 
plate-glass,  the  loss  of  live  stock,  and  the  dishonesty  of  employees. 

390.  An  Insurance  Company  is  a  company  or  corporation 
which  insures  against  loss  or  damage. 

Insurance  companies  usually  make  a  specialty  of  a  certain  kind  of  insur- 
ance, as  Fire,  Marine,  Life,  Accident,  etc.  Certain  companies  combine  Fire 
and  Marine  Insurance,  while  some  of  the  large  English  companies  have  Fire, 
Marine,  and  Life  departments. 

391.  Insurance  companies  may  be  classified  according  to  prin- 
ciples  of  organization   as   follows:  —  1,   Stock;    2,   Mutual;   3, 
Mixed,  or  Stock  and  Mutual. 

Of  the  188  Fire  (126),  Fire-Marine  (49),  and  Marine  (13)  insurance  com- 
panies doing  business  in  the  State  of  New  York  in  1879,  165  were  Stock,  11 
Mixed  (Stock  and  Mutual),  and  12  purely  Mutual.  Their  net  assets,  Dec.  81, 
1879,  were  $150,600,689  ;  amount  of  risks  in  force,  $6,997,419,444. 

The  above  does  not  include  many  town  and  county  co-operative  insurance 
companies. 

392.  A  Stock  Insurance  Company  is  one  in  which  the 
capital  is  owned  by  individuals,  called  stockholders.     They  alone 
share  the  profits  and  are  liable  for  the  losses. 


INSURANCE.  167 

The  business  of  a  stock  company  and  also  of  a  mixed  company,  is  managed 
by  directors  chosen  by  the  stockholders.  No  policyholder,  unless  a  stock- 
holder, has  any  voice  in  any  way  in  the  election  of  the  officers,  or  in  the 
management  of  its  business. 

393.  A  Mutual  Insurance   Company  is  one  in  which 
there  are  no  stockholders,  and  the  profits  and  losses  are  shared 
among  those  who  are  insured  (the  policyholders). 

Non-participating  policies,  the  holders  of  which  do  not  share  in  the 
profits  or  losses,  are  issued  by  certain  mutual  and  mixed  companies. 

394.  A  Mixed  Insurance  Company  is  one  which  is  con- 
ducted upon  a  combination  of  the  stock  and  mutual  plan. 

Usually  in  a  mixed  company,  all  profits  above  a  limited  dividend  to  the 
stockholders  are  divided  among  the  participating  policyholders. 

395.  The  Policy  is  the  written  contract  between  the  Insur- 
ance Company  (the  Insurer  or  Underwriter)  and  the  Insured.     It 
contains  a  description  of  the  property  insured,  the  amount  of 
the  insurance,  and  the   conditions  under  which  the  policy  is 
issued,  etc. 

396.  The  Premium  is  the  amount  paid  for  the  insurance. 

1.  Premium  rates  are  expressed  by  giving  the  cost  in  cents  of  $100  insur- 
ance.    The  rate  is  sometimes  expressed  as  a  certain  per  cent,  of  the  amount  of 
the  risk.     Thus,  a  rate  of  75  cents  per  $100  is  equivalent  to  \%. 

2.  The  premium  rates  depend  upon  the  nature  of  the  risk,  and  the  length 
of  time  for  which  the  policy  is  issued. 

8.  A  fee  of  $1,  or  $1.25,  is  sometimes  charged  for  the  policy  in  addition 
to  the  premium. 

397.  An  Insurance  Agent  is  a  person  who  represents  an 
insurance  company  or  several  companies,  and  acts  for  them  in 
soliciting  business,  collecting  premiums,  adjusting  losses,  etc. 

398.  An  Insurance  Broker  is  a  person  who  effects  insur- 
ance, for  negotiating  which  he  receives  a  commission  or  brokerage 
from  the  company  taking  the  risk. 

Brokers  are  regarded  as  agents  of  the  insured,  and  not  of  the  insurance 
company. 

399.  The  Surplus  of  an  insurance  company  is  the  excess  of 
the  assets  over  the  liabilities  (including  capital  and  unearned 
premium). 


168  INSURANCE. 


FIRE     INSURANCE. 

400.  Fire   Insurance  refers  to  insurance  against  loss   or 
damage  by  fire. 

Fire  policies  are  usually  issued  for  periods  of  from  1  to  5  years.  Certain 
companies  issue  policies  for  longer  periods.  Of  the  outstanding  risks  of  the 
largest  insurance  company  of  New  York,  Dec.  31,  1879,  about  50  %  were  for 
1  year  or  less,  2%  for  2  years,  2S%  for  3  years,  4^  for  4  years,  and  16$  for 
5  years. 

401.  Adjustment  of  Losses. — In  an  ordinary  fire  insur- 
ance policy,  a  person  who  insures  will  be  paid  the  extent  of  his 
loss  up  to  the  amount  of  his  insurance ;  but  in  policies  contain- 
ing the  "average  clause,"  the  payment  is  such  proportion   of 
the  loss  as  the  amount  of  the  insurance  bears  to  the  total  value 
of  the  property. 

1.  The  following  is  the  usual  form  of  the   "average  clause"   above 
referred  to :  "  It  is  a  condition  of  this  insurance,  that  if  the  whole  value  of 
the  above  described  property,  contained  in  any  or  all  of  the  above  mentioned 
buildings  and  premises,  shall  exceed  the  whole  amount  of  insurance  thereon, 
then,  in  case  of  loss  or  damage  by  fire,  this  policy  shall  contribute  to  the 
payment  of  said  loss  or  damage  in  the  proportion  only  that  the  whole  amount 
of  insurance  on  said  property  shall  bear  to  the  whole  value  of  said  property, 
in  all  of  said  buildings,  at  the  time  said  loss  or  damage  may  occur." 

2.  Under  a  policy  containing    the  "  average    clause,"  a    person   who 
insures  $5000  on  property  worth  $10000,  would  receive  only  $2500  in  case 
of  an  actual  loss  of  $5000  ;    $1500  in  a  loss  of  $3000 ;    $4000  in  a  loss  of 


3.  Insurance  companies  usually  reserve  the  privilege  of  replacing  or 
repairing  the  damaged  premises. 

402.  A  Floating  Policy  is  one  which  covers  property  stored 
in  several  buildings  or  places.    The  name  is  applied  more  particu- 
larly to  policies  which  cover  goods  whose  location  may  be  changed 
in  process  of  manufacture  or  in  the  ordinary  course  of  business. 
The   "average  clause"  is  a  usual  condition  of  policies  of  this 
class. 

403.  Short  Rates  are  rates  for  a  term  less  than  a  year. 

If  an  insurance  policy  is  terminated  at  the  request  of  the  policy  holder, 
the  company  retains  the  customary  "  short  rates  "  for  the  time  the  policy  has 
been  in  force  ;  if  terminated  at  the  option  of  the  company,  a  ratable  propor- 
tion of  the  premium  is  refunded  for  the  unexpired  term  of  the  policy. 


MARINE    INSURANCE.  169 


MARINE     INSURANCE. 

404.  Marine  Insurance  refers  to  insurance  of  vessels  and 
their  cargoes  against  the  dangers  of  navigation. 

1.  Inland    and    Transit    Insurance  refer  to  insurance   of   merchandise 
while  being  transported  from  place  to  place  either  by  rail  or  water  routes, 
or  both. 

2.  Policies  on  cargoes  are  issued  for  a  certain  voyage,  or  from  port  to 
port,  and  on  vessels  for  a  specified  time  or  for  a  certain  voyage. 

3.  The  particular  average  clause  is  the  clause  which  exempts  the  insur- 
ance company  from  the  payment  of  any  partial  loss  or  particular  average, 
unless  it  exceeds  a  certain    per   cent,  of  the  value  of  the  property.     The 
particular  average  clause  is  sometimes  applied  to  the  value  of  each  parcel  or 
series  of  parcels,  according  to  invoice  numbers. 

4.  Insurance  Certificates,  showing  that  certain  property  has  been  insured, 
and  stating  the  amount  of  the  insurance  and  the  name  of  the  party  abroad 
who  is  authorized  to  make  the  settlement,  are  issued  by  marine  companies. 
They  are  negotiable,  and  are  usually  sent  to  the  consignee  of  the  merchandise 
to  make  the  loss  payable  at  the  port  of  destination,  and  to  otherwise  facilitate 
the  adjustment  of  the  insurance  in  case  of  loss. 

405.  Adjustment   of  Losses. — In  marine  insurance,  in 
case  of  loss  or  damage,  the  insurance  company  contributes  such 
proportion  of  the  loss  as  the  amount  of  the  insurance  bears  to  the 
total  value  of  the  property. 

1.  The  adjustment  of  marine  policies  in  case  of  loss  is  on  the  same 
principle  as  the  adjustment  of  fire  policies  containing  the  "average  clause  " 
(401,  1). 

2.  In  the  adjustment  of  marine  losses,  the  pound  sterling  is  usually 
estimated  at  $4.95. 

406.  An  Open  Policy  is  one  upon  which  additional  insur- 
ances may  be  entered  at  different  times.     It  covers  merchandise 
which  may  be  shipped  on  "Vessel  or  Vessels"  from  "Ports  and 

*  Places"  to  "Ports  and  Places/'  for  amounts  "as  endorsed  "and 
at  rates  "as  agreed." 

1.  The  date  of  the  shipment,  name  of  vessel,  ports  of  shipment  and 
destination,  the  amount  of  the  insurance,  rate,  premium,  and  a  description 
of  the  property  are  entered  on  the  policy  or  in  a  pass-book,  which  is  regarded 
as  part  of  the  policy.    (See  Ex.  29,  Art.  4O7.) 

2.  Open  policies  with  pass-books  attached  and    insuring  merchandise 
against  loss  or  dainags  by  fire,  are  issued  by  fire  insurance  companies. 


170  INSURANCE. 

3.  Open  policies,  which  cover  all  risks  whether  accepted  and  endorsed  on 
the  policy  or  not,  are  issued  to  merchants  who  are  receiving  merchandise  from 
foreign  countries,  and  who  do  not  always  have  a  definite  knowledge  of  the 
time  and  mode  of   shipment.     Such  policies  usually  contain  the  following 
clause  :  "  The  company  are  to  be  entitled  to  premiums  at  their  usual  rates  on 
all  shipments  reported  or  not.     It  is  warranted  by  the  assured  to  report  every 
shipment  on  the  day  of  receiving  advice  thereof,  or  as  soon  thereafter  as 
practicable,  when  the  rate  of  premium  shall  be  fixed  by  the  President  or  Vice- 
President  of  the  Company. " 

The  above  policies  cover  the  invoice  cost  and  10%  additional  until  the 
amount  of  the  risk  is  endorsed  on  the  policy  or  pass-book. 

4.  Open  policies  are  sometimes  issued  which  cover  only  such  risks  as 
may  be  accepted  and  endorsed  on  the  policy  by  the  company. 


EXAMPLES. 

4O7.  I.  A  building  was  insured  for  $2500  in  one  company  at 
and  for  $5000  in  another  company  at  125  cents.     What  was 
the  total  premium  paid? 

2.  A  cargo  of  goods  was  insured  for  $9000  at  \%.     What  was 
the  cost  of  the  insurance,  $1.25  being  charged  for  the  policy  ? 

3.  What  is  the  total  premium  of  the  following  insurances  : 
$5000  at  \\%  for  2  years,  $7000  at  450  for  5  years,  $1500  at  \%  for 
4  years,  $2000  at  5%  for  7  years,  $3500  at  450  for  1  year,  $2000  at 
700  for  4  years,  $4000  at  \\%  for   5  years,    $2000  at    600   for 
4  years,  $4500  at  250  for  2  years,  $3600  at  1250  for  1  year,  and 
$3000  at  240^  for  4  years  ? 

4.  $20  were  paid  for  an  insurance  of  $2500 ;   what  was  the 
premium  rate  ? 

5.  $25.20  were  paid  for  an  insurance  at  the  rate  of  700  per 
$100.     What  was  the  amount  of  the  risk  ? 

6.  A  factory  was  insured  for  $7500  for  1  year  at  2-j%  stock  for 
$2500  at  2£%,  and  raw  material  for  $2500  at  l%%.     What  was  the 
total  premium  ? 

7.  What  is  the  cost  of  insuring  a  house  for  $5000  at  the  rate 
of  45^  per  $100  ? 

8.  A  cargo  of  merchandise  was  insured  for  $6500  at  \%,  includ- 
ing the  risk  of  fire  while  on  wharf  awaiting  shipment.     What  was 
the  premium? 

9.  A  building  was  insured  Jan.  1,  1880,  for  $2000,  for  7  years, 
at  5%  ;   what  was  the  value  of  the  unearned  premium,  Jan.  1, 
1882? 


EXAMPLES.  171 

10.  A  shipment  of  goods  was  insured  in  the  Pacific  Mutual 
Insurance  Co.  for  $9600  at  750  less  20%  in  lieu  of  scrip  and  inter- 
est.    What  was  the  net  cost  of  the  insurance  ? 

11.  A  house  was  insured  for  $5000  for  4  years  at  600  per 
annum.     The  house  was  destroyed  by  fire.    What  was  the  actual 
loss  of  the  company,  making  no  allowance  for  interest  ? 

12.  Suppose  the  above  house  was  worth  $8000.     What  was  the 
actual  loss  of  the  owners  ? 

13.  A  cargo  of  hides  from  Montevideo  to  New  York  having 
increased  in  value  since  the  insurance  was  effected,  the  anticipated 
profits  were  insured  for  $3000  at  If  %  less  20%.     What  was  the 
premium  ? 

14.  A  factory  (worth  $3000)  and  its  contents  are  insured  for 
$10000  as  follows  :  $2000  on  building,  $3000  on  machinery  (worth 
$5000),   and  $5000  on  stock  (worth  $8000).      The   building  is 
damaged  by  fire  to  the  amount  of  $1000,  the  machinery  $4000, 
and  stock  is  a  total  loss.     How  much  is  the  claim  against  the 
insurance  company  ? 

15.  A  cargo  of  goods  valued  at  $20000  was  insured  for  $12000. 
If  the  goods  were  damaged  to  the  amount  of  $15000,  how  much 
of  the  loss  would  be  paid  by  the  insurance  company  ?  (Art.  4O5.) 

16.  A  building  is  insured  in  several  companies  for  $60000,  and 
is  damaged  by  fire  to  the  extent  of  $24000.     What  per  cent,  of  its 
risk  is  paid  by  each  company  ? 

17.  A  stock  of  goods  was  insured,  May  1,  for  1  year,  for  $6000, 
at  90^.     The  policy  was  cancelled  Nov.  1,  at  the  request  of  the 
insured.     How  much  was  the  return  premium,  the  short  rate  for 
6  months  being  630  ?     How  much  would  have  been  returned  by 
the  company,  if  the  policy  had  been  cancelled  at  its  request  ? 

18.  A  quantity  of  merchandise  valued  at  $6000  is  insured  for 
$5000.     It  is  damaged  by  fire  to  the  amount  of  $1728.     How 
much  of  the  loss  is  paid  by  the  insurance  company,  the  policy 
containing  the  "average  clause"  (4O1)? 

19.  What  was  paid  for  insuring  a  cargo  of  merchandise  for 
$8750  at  \%  less  20%  ? 

20.  A  marine  rate  of  %%  for  a  voyage  of  10  days  is  equivalent 
to  what  rate  per  annum  ? 

21.  What  were  the  average  net  assets  for  every  $100  insured 
of  the  F.  F.-M.,  and  M.  Ins.  Cos.,  doing  business  in  the  State  of 
New  York  in  1879  ?     (See  Art.  391,  Note.) 


172 


INSURANCE. 


22.  A  factory  and  its  contents  are  insured  for  $5000  in  com- 
pany M,  $5000  in  N,  $5000  in  0,  $4000  in  P,  and  $2500  in  each 
of  the  following  companies :    Q,  K,  S,  T,  II,  V,  W,  X,  Y,  and  Z. 
What  was  the  total  premium,  the  rate  being  2^  less  10$  ? 

23.  The   above   insurance   covered   the    following    property : 
$4000  on  building  marked  A  on  plan,  $4000  on  B,  $5000  on  C, 
$500  on  D,  $500  on  E,  $3500  on  stock  and  materials  in  building 
marked  A  on  plan,  $8000  on  machinery,  etc.,  in  A,  $11500  on 
stock  and  materials  in  B  and  C,  $4000  on  machinery,  etc.,  in  B 
and  C,  $2500  on  horses  in  D,  $500  on  harness,  hay,  feed,  etc., 
in  D.     Suppose  building  A  and  its  contents  were  totally  destroyed 
by  fire,  what  would  be  the  loss  of  company  M  ?     Of  P  ?     Of  T  ? 

NOTE.— The  above  insurance  was  divided  pro  rata  among  the  several 
companies,  each  policy  designating  the  exact  amount  on  each  building,  etc. 

24.  In  the  above  example,  what  is  the  amount  of  the  risk  of 
company  M  on  the  building  marked  A  on  plan  ?     On  C  ? 

25.  The  net  invoice  value  of  a  quantity  of  goods  is  $6325,  and 
the  insured  value  $6500.     The  insured  value  is  what  per  cent, 
greater  than  the  invoice  value? 

26.  A  quantity  of  merchandise  valued  at  $9035,  is  insured  for 
$9000.     What  is  the  insurance  on  part  of  the  same,  the  estimated 
value  being  $2638  ? 

27.  If  500  packages  of  merchandise  are  insured  for  $2627.78, 
what  is  the  insurance  on  60  packages  ? 

28.  The  estimated  sound  value  of  a  quantity  of  merchandise, 
damaged  at  sea,  was  $328.55,  and  the  proceeds  when  sold  at  auc- 
tion, $299.35.     How  much  of  the  loss  was  shared  by  the  Insurance 
Co.,  the  insurance  having  been  $315.33  ? 

29.  Make  the  extensions  of  the  following  "open  policy"  and 
find  the  total  amount. 


Date. 

Name  of 
vessel. 

From. 

To. 

On. 

1^ 

Rate. 

~Ha 

0  f\5 
|oS 

1881. 
Sept.    2 

Othello. 

N.  Y.  via  Hull. 

Stockholm. 

50Ba.Mdse. 

5100 

H 

**4*# 

"      7 

Algeria. 

New  York. 

Liverpool. 

68  " 

6675 

* 

s-^** 

."    16 

Germanic. 

New  York. 

Liverpool. 

92  " 

13500 

i 

*#>** 

"    17 

Rialto. 

N.  Y.  via  Hull. 

Christiania. 

6  " 

600 

i 

•H-^ 

"    23 

Otranto. 

N.Y.  via  Hull. 

Orebro. 

30  " 

2700 

T,PSS  < 

H 
>,n# 

#*  ** 

$*##  *# 
• 
#•*  #* 

EXAMPLES. 


173 


30.   Claim  of  Shultz,  South  wick  &  Co.,  for  partial  loss  on  mer- 
chandise, per  "Lessing,"  from  New  York  to  Hamburg,  Feb.  24, 

1882. 

Insured  value  of  cargo      .        . '              .  $10000 

Net  invoice  value 9696 

Advance    .  ***  =  ****%. 


Marks 
and 
Num- 
bers. 

No.  of 
pkgs 
shipped. 

Invoice 
weight 

Invoice 
value. 

No.  of 

damaged. 

Propor- 
tional 
invoice 
weight. 

Propor- 
tional 
invoice 
value. 

Advance 
at 

*.**"% 

Insured 
value  of 
damaged. 

Sound 
wt., 
Germ. 
Ibs.t 

H  R 

251 

550 

9497 

28^ 

233 

4023 

1146.55 

3621 

2 

150 

3357 

28£ 

46 

1029 

293.26 

927 

3 

275 

4702 

27| 

118 

2018 

554.95 

1817 

# 

* 

# 

* 

# 

# 

# 

* 

2001 

1071 

$5137.03 

&***_*•* 

$****.** 

16792 

Sound  weight  16792  Ibs.  -223  Iba.  (Tare)  =*****  tts.  @  1.35  Rm.=Rm. 

Less  discount  1  %  .     .     .     . 
Sound  value,      .     .     .      Rm? 
Gross  proceeds  at  auction     . 
Loss     ......      Rm. 


******* 
***** 


******* 
14729.81 


**** 


Loss  =  **.**%  of  sound  value. 

Insured  value  of  damaged  $****.  ** 

Charges,   .     .     .     Rm.    201.32 

Inspection     ....     185.44 

Agents'  fees,       .     .     .     22_3__     Rm.  *****  @  24*  = 

Total  claim    . 


$***. 


31.  The  total  paid-up  capital  of  the  joint-stock  fire  and  fire- 
marine  companies  doing  business  in  the  State  of  New  York 
(excepting  foreign  companies),  Dec.  31,  1879,  was  $50,992,220, 
and  the  surplus  $34,998,146.  The  total  surplus  was  what  per 
cent,  of  the  total  capital  ? 

82.  The  above  companies,  with  the  exception  of  the  New 
York  Mutuals  (6),  during  the  year  1879,  received  $69,657,129  in 
gross  premiums  for  insuring  $7,991,450,000.  What  was  the 
average  premium  for  every  $100  insured  ? 

33.  Dec.  31,  1879,  the  capital  stock  of  the  Insurance  Co.  of 
N.  A.,  Philadelphia,  Pa.,  was  12,000,000;  surplus,  $2,338' 378 ; 
dividend  paid  during  1879,  $400,000.  The  surplus  is  what  per 
cent,  of  the  capital  stock  ?  The  dividend  is  what  per  cent,  of  the 
capital,  and  of  the  capital  and  surplus  ? 

t  Sae  Art.  243. 


EXCHANGE. 


DEFINITIONS. 

408.  Exchange  is  the  system  by  which  merchants  in  distant 
places  discharge  their  debts  to  each  other  without  the  transmission 
of  money. 

Suppose,  for  example,  A  of  New  York  owes  B  of  Chicago  $1000  for 
grain,  and  C  of  Chicago  owes  D  of  New  York  $1000  for  dry  goods.  The  two 
debts  may  be  discharged  by  means  of  one  draft  or  bill  of  exchange  without 
the  transmission  of  money.  Thus,  B  of  Chicago  draws  on  A  of  New  York 
for  $1000,  and  sells  the  draft  to  C  of  Chicago  who  remits  it  to  D  of  New  York. 
D  of  New  York  presents  the  draft  to  A  of  New  York  for  acceptance  or  pay- 
ment, and  thus  both  debts  are  cancelled.  There  is  in  effect  a  sstting-off  or 
exchange  of  one  debt  for  the  other. 

The  business  of  exchange  is  usually  conducted  through  the  medium  of 
banks  and  bankers,  who  buy  commercial  bills  and  transmit  them  for  credit  to 
the  places  on  which  they  are  drawn.  They  also  sell  their  own  drafts  on  their 
correspondents  in  any  amounts  demanded. 

409.  A  Bill  of  Exchange,  or  Draft,  is  an  order  or  request 
addressed  by  one  person  (the  Drawer)  to  another  (the  Drawee), 
directing  the  payment  of  a  specified  sum  of  money  to  a  third 
person  (the  Payee)  or  to  his  order.    It  is  issued  at  one  place  and 
payable  at  another.     (See  Art.  352,  5-6.) 

For  brevity,  bills  of  exchange  are  frequently  called  "  exchange." 
According  to  the  laws  cf  most  States,  drafts  drawn  in  one  State  and  pay- 
able in  another,  are  termed  foreign  bills  of  exchange.     For  the  purposes  of 
this  book,  the  term  "  domestic  exchange  "  will  be  applied  to  bills  drawn  and 
payable  in  the  United  States. 

410.  Bills  of  exchange  are  of  two  kinds,  Inland  or  Domestic, 
and  Foreign. 

411.  A  Domestic  or  Inland  Bill  of  Exchange  is  one 
which  is  payable  in  the  same,  country  in  which  it  is  drawn. 


DOMESTIC    EXCHANGE.  175 

412.  A  Foreign  Bill  of  Exchange  is  one  which  is  payable 
in  a  different  country  from  the  one  in  which  it  is  drawn  ;  as  a 
draft  drawn  in  the  United  States  and  payable  in  England. 

413.  When  drafts  sell  for  more  than  their  face  value,  exchange 
is  above  par  or  at  a  premium  ;  when  for  less  than  their  face,  below 
par  or  at  a  discount. 

When  Chicago  owes  New  York  the  same  amount  that  New  York  owes 
Chicago,  exchange  will  be  at  par  ;  that  is,  drafts  will  sell  at  their  face  value. 
When  Chicago  owes  New  York  more  than  New  York  owes  Chicago,  drafts  on 
New  York  will  sell  at  a  premium  ;  there  will  be  more  buyers  of  exchange 
than  sellers,  and  drafts  will  sell  for  more  than  their  face  value.  When  Chicago 
owes  New  York  less  than  New  York  owes  Chicago,  the  demand  in  Chicago 
for  drafts  on  New  York  will  be  less  than  the  supply,  and  drafts  will  sell  for 
less  than  their  face  value,  or  at  a  discount. 


DOMESTIC     EXCHANGE. 

414.  Domestic  or  Inland  Exchange  relates  to  drafts  drawn 
at  one  place  on  another  in  the  same  country. 

415.  The  domestic   exchanges  on  New  York  at  the  places 
named  were  quoted  as  follows,  May  7,  1881  :   Savannah,  -J-  @  -f 
premium;  Charleston,  -J  @  £  premium;  New  Orleans,  $1.50  @ 
$2.50  premium;  St.  Louis,  25  cents  premium  ;  Chicago,  50  @  75 
cents  premium  ;  and  Boston,  25  cents  discount. 

1.  At  Savannah  and  Charleston  the  rates  per  cent,  of  the  premium  or 
discount  are  given.     Thus,  when  exchange  is  quoted  at  £  premium,  a  draft  of 
$100  may  be  purchased  for  $100^  ($100.25). 

2.  At  New  Orleans,  St.  Louis,  Chicago,  and  Boston,  the  premium  or  dis- 
count per  $1000  is  given.     Thus,  a  draft  of  $1000  at  $2.50  premium  may  be 
purchased  for   $1002.50.      $2.50  per  $1000   premium   is   equivalent  to  \% 
premium. 

3.  The  selling  rates  are  about  \%   ($1.25)  higher  than  the  buying  rates, 
and  bankers'  exchange  is  usually  higher  than  commercial. 

4.  The  rate  of  domestic  exchange  is  limited  by  the  cost  of  shipping  gold 
or  currency  by  express,  and  the  premium  or  discount  will  not  exceed  this  cost. 
Thus,  if  a  merchant  in  Chicago  is  charged  a  premium  of  $10  for  a  draft  of 
$10000,  and  he  can  send  the  currency  by  express  for  $7.50,  it  will  be  to  his 
advantage  to  remit  by  the  latter  method. 

The  following  appeared  in  a  New  York  financial  paper,  May  8,  1881,  the 
date  of  the  above  quotations:  —  "The  domestic  exchanges  at  the  West  are 
sufficiently  high  to  permit  of  a  movement  of  funds  Eastward,  but  at  the  East, 


176  EXCHANGE. 

New  York  funds  are  still  at  a  discount  and  some  shipments  of  gold  and 
currency  continue  to  be  made  to  the  Eastern  cities." 

5.  The  preceding  quotations  refer  to  sight  exchange.  Time  drafts  are  dis- 
counted in  the  same  manner  as  promissory  notes.  In  certain  cases  bankers  in 
discounting  notes  and  drafts  payable  in  distant  places,  charge  interest  for  the 
time  required  for  the  return  of  the  money  when  the  note  or  draft  is  paid  ;  and 
in  the  case  of  drafts  drawn  a  certain  number  of  days  after  sight,  bankers 
sometimes  charge  interest  for  the  time  required  for  the  acceptance  of  the 
drafts.  Thus,  if  a  draft  was  drawn  in  New  York  on  St.  Louis  and  payable 
CO  days  after  sight,  it  would  require,  in  the  ordinary  course  of  the  mails,  3 
days  for  the  acceptance  of  the  draft.  The  draft  would  be  paid  in  63  days 
(including  the  days  of  grace),  and  3  days  would  elapse  before  the  money 
would  be  returned  to  New  York.  The  banker  would  be  justified  in  charging 
interest  for  69  days,  the  interval  between  the  day  he  advanced  the  money  in 
New  York,  and  the  day  it  was  returned  to  him  again.  If  the  draft  was  drawn 
on  San  Francisco,  fully  19  days  (8  days  for  the  acceptance,  3  days  of  grace, 
and  8  days  for  the  return  of  the  money)  would  be  added  to  the  time  of  the 
draft.  Between  New  York  and  San  Francisco  and  other  distant  places,  money 
is  frequently  transferred  by  telegraph. 

EXAMPLES. 

416.  1.  What  is  the  value  in  Savannah  of  a  draft  on  New 
York  for  $8750  at  \%  premium  ? 

2.  Find  the  cost  in  New  Orleans  of  a  draft  on  New  York  for 
$8375  at  $2.50  premium. 

Find  the  value  of  the  following  drafts  : 

Face.  Exchange.  Face.  Exchange. 

S.  $5000,  \%  premium.  £.$4287.75,         15?  discount. 

4.  $4375,  \%  discount.  9.  $3416.33,         25^  premium. 

5.  $8417,  $$  premium.  10.  $2825.49,    $1.25    discount. 

6.  $9873,  |%  premium.  11.  $9873.62,    $2.50    premium. 

7.  $5284,  £%  discount.  ^.$8412.75,         75^  discount. 
13.  A  of  Chicago  buys  cattle  for  B   of  New  York  to  the 

amount  of  $9858.07.  How  large  a  draft  should  be  drawn  on  B, 
so  that  when  sold  at  a  discount  of  50^  (-fa%)9  the  proceeds  would 
be  sufficient  to  pay  the  bill  ? 

NOTE. — To  find  the  face  of  a  draft,  instead  of  dividing  the  value  of  the 
draft  by  the  rate  of  exchange  (in  the  above  example,  .99|g-  or  .9995),  business 
men  and  bankers  calculate  the  premium  or  discount  on  the  value  of  the  draft, 
and  subtract  or  add  it  to  the  value  as  the  case  requires.  Thus,  in  the  above 
example,  the  discount  would  be  *  of  TV%  of  $9858.07,  or  $4.93,  which  added 
to  the  given  proceeds  would  produce  the  face  $9863.  This  method  produces 
too  small  a  result  in  all  cases,  the  error  being  equivalent  to  the  percentage  of 
the  premium  or  discount.  In  this  example  the  error  is  less  than  £  cent. 


DOMESTIC   EXCHAN  G  E.  177 

For  ordinary  examples  in  business,  the  foregoing  method  is  sufficiently 
accurate.  At  \  % ,  or  $5.00  (a  very  high  rate  for  domestic  exchange)  on  a  draft 
whose  value  is  $10000,  the  error  would  be  only  25  cents.  If  greater  accuracy 
is  required,  the  necessary  correction  can  be  made  by  adding  the  percentage 
of  the  premium  or  discount.  Thus,  if  the  value  of  the  draft  is  $10000,  and 
exchange  is  \%  discount,  the  face  would  be  $10000  +  $50  (\%  of  $10000) 
f  $0.25  (\%  of  $50)  —  $10050.25.  If  at  \%  premium,  the  face  would  be 
$10000  -  $50  +  $0.25  =  $9950.25. 

By  the  above  method,  find  the  face  of  the  following  drafts : 

Value.  Exchange.  Value.  Exchange. 

34.  $1876.16,  \%  premium.  19.  $7375,  250  premium. 

.  15.  $2437.75,  ^discount.  £0.  $9218,  500  discount. 

16.  $3342.38,  \%  discount.  21.  $6438,  $1.00    premium. 

17.  $2238.42,  -J^  premium.  22.  $9243,  $1.25    premium. 

18.  $8175.50,  \%  premium.  28.  $5280.  750  discount. 

24.  A  of  New  Orleans  being  indebted  to  B  of  New  York 
$9316.75,  forwards  to  him  a  check  on  a  New  Orleans  bank  for 
that  amount,  to  cash  which  B  is  obliged  to  allow  a  discount  of 
%%.     How  much  does  A  still  owe  B,  and  for  what  amount  should 
the  check  have  been  drawn  to  net  B  the  amount  due  ? 

25.  What  is  the  value  of  a  draft  on  New  York  for  $3000, 
payable  in  60  days  (63  days)  after  date  (353,  8),  exchange  being 
J%  premium,  and  interest  6$? 

NOTE. — From  the  face  of  the  draft,  subtract  the  interest,  and  to  the 
result  add  the  exchange. 

26.  Find  the  proceeds  of  a  draft  drawn  at  Chicago  on  New 
York  for  $12000,  and  payable  90  days  after  sight,  exchange  500 
discount,  interest  5%,   and  allowing  3  days   additional  for  the 
acceptance  of  the  draft. 

27.  A  banker  in  New  York  discounts  a  draft  for  $8000,  pay- 
able in  San  Francisco  60  days  after  sight ;  what  would  be  the 
proceeds,  exchange  being  \%  discount,  interest  6$,  and  allowing 
8   days  for  the   acceptance   and   8  days  for  the  return   of  the 
money  ? 

28.  A  merchant  paid  $6920.64  in  Charleston  for  a  sight  draft 
of  $6912  ;  what  was  the  rate  of  exchange  ? 

29.  A  commission  merchant  sold  13475  pounds  of  leather  at 
26f  cents  a  pound.     If  his  commission  is  5%,  and  exchange  \% 
premium,  how  large  a  draft  can  he  buy  to  remit  to  the  consignor  ? 

SO.  How  large  a  60-days'  draft  must  I  draw,  so  that  when  sold 
it  will  produce.  $10000,  exchange  \%  discount,  interest 
12 


178  EXCHANGE. 


FOREIGN     EXCHANGE. 

417.  Foreign  Exchange  relates  to  drafts  or  bills  of  exchange 
drawn  in  one  country  and  payable  in  another. 

Foreign  bills  of  exchange  are  usually  drawn  in  the  moneys  of  account  of 
the  countries  in  which  they  are  payable.  Thus,  drafts  on  England  are  usually 
drawn  in  pounds,  shillings,  and  pence  ;  on  France,  Belgium  and  Switzerland, 
in  francs  ;  on  Germany,  in  marks  ;  on  the  Netherlands  (Holland),  in  guilders. 

Foreign  bills  of  exchange  are  usually  drawn  at  sight  (3  days)  or  at 
sixty  (63  days)  days'  sight.  Sight  drafts  are  frequently  called  "short" 
exchange,  and  60  day  drafts,  "  long"  exchange.  "Long"  exchange  is  sold 
at  a  rate  below  that  for  "  short  "  exchange,  sufficient  to  equalize  the  difference 
in  interest  between  the  dates  of  maturity  of  the  two  classes  of  bills. 

418.  To  secure  safety  and  speed  in  the  transmission  of  foreign 
bills  of  exchange,  they  are  drawn  in  sets  of  two  or  three  of  the 
same  tenor  and  date.     The  separate  bills  are  sent  by  different 
steamers,  and  when  any  one  of  them  is  paid,  the  others  become 
void.     Some  merchants  send  only  the  first  and  second,  and  pre- 
serve the  third. 

SET    OF     EXCHANGE. 


EXCHANGE  FOR  £1000.  NEW  YORK,  May  16,  1882. 

Sixty  days  after  sight  of  this  FIRST  of  Exchange  (Second  and 
Third  unpaid),  pay  to  the  order  of  A.  T.  STEWART  &  Co.,  One 
Thousand  Pounds  Sterling,  value  received,  and  charge  the  same 
to  account  of 

No.  1738.  BROWN  BROTHERS  &  Co. 

To  BROWN,  SHIPLEY  &  Co., 
London,  England. 

(2.) 
EXCHANGE  FOR  £1000.  NEW  YORK,  May  16,  1882. 

Sixty  days  after  sight  of  this  SECOND  of  Exchange  (First  and 
Third  unpaid),  pay  to  the  order  of  A.  T.  STEWART  &  Co.,  One 
Thousand  Pounds  Sterling,  value  received,  and  charge  the  same 
to  account  of 

No.  1738.  BROWN  BROTHERS  &  Co. 

To  BROWN,  SHIPLEY  &  Co.,  ) 
London,  England.       J 


FOREIGN   EXCHANGE.  179 

(3.) 
EXCHANGE  FOB  £1000.  NEW  YORK,  May  16,  1882. 

Sixty  days  after  sight  of  this  THIED  of  Exchange  (First  and 
Second  unpaid),  pay  to  the  order  of  A.  T.  STEWART  &  Co.,  One 
Thousand  Pounds  Sterling,  value  received,  and  charge  the  same 
to  account  of 

No.  1738.  BROW^  BROTHERS  &  Co. 

To  BROW^,  SHIPLEY  &  Co.,  j 
London,  England.      j 

419.  A  Letter  of  Credit  is  an  instrument  issued  by  a 
banker  and  addressed  to  bankers  generally,  by  which  the  holder 
may  draw  funds  at  different  places  and  in  amounts  to  suit  his  con- 
venience, the  total  amount  drawn  not  exceeding  the  limit  of  the 
letter  of  credit. 

A  bill  of  exchange  is  payable  at  a  certain  place,  at  a  certain  fixed  time, 
and  for  a  certain  amount,  while  a  letter  of  credit  is  payable  at  different  places, 
at  different  times,  and  in  different  amounts. 

A  person,  who  intends  to  travel  in  foreign  countries,  may  procure  a  letter 
of  credit  by  depositing  either  cash  or  securities  with  a  foreign  exchange 
banker  for  the  amount  of  the  letter.  When  the  American  banker  is  notified 
of  the  payment  of  the  traveler's  drafts  in  London,  he  debits  the  account  of 
the  holder  of  the  letter  of  credit  with  the  amount  drawn  and  the  charges,  at 
the  current  rate  of  exchange.  A  small  rate  of  interest  is  allowed  on  the 
account,  and  a  settlement  is  made  on  the  return  of  the  traveler. 

If  a  person  has  business  connections,  he  may  avoid  making  a  deposit  by 
having  some  commercial  firm  sign  a  bond  as  security.  By  this  method,  when 
the  New  York  banker  is  notified  of  the  payment  of  the  traveler's  draft  in 
London,  he  immediately  draws  a  sight  draft  (42O)  for  the  amount  and  the 
charges  (42O)  on  the  traveler's  representative,  and  no  account  is  kept  with 
the  traveler  on  the  books  of  the  banker.  In  this  case,  a  settlement  is  made 
with  the  commercial  house  on  the  return  of  the  traveler. 

The  holder  of  a  letter  of  credit  desiring  funds,  presents  it  to  a  banker  at 
the  place  he  may  be  visiting.  The  banker  will  prepare  a  sight  draft,  which  the 
holder  of  the  letter  will  sign,  on  the  London  banker  mentioned  in  the  letter 
of  credit.  If  the  signature  on  the  draft  and  on  the  letter  of  credit  correspond, 
the  draft  will  be  cashed  by  the  banker  at  the  current  rate  of  exchange.  The 
bankers  who  cash  the  drafts  of  the  holder  of  the  letter,  write  the  date  of  pay- 
ment, their  names,  and  the  amounts  drawn  (in  words  and  figures),  on  the 
back  of  the  letter  of  credit.  When  the  London  banker  pays  the  drafts,  he 
immediately  notifies  the  American  banker  (the  issuer  of  the  letter  of 
credit).  The  foreign  bankers  mentioned  as  correspondents  in  a  Letter  of 
Credit  are  bound  to  honor  the  drafts  of  the  holder ;  but  other  banks  and 
agencies  where  the  parties  are  known,  are  also  free  to  respond. 


180 


EXCHANGE. 


BROWN    BROTHERS    &    Co/s    CIRCULAR    LETTER    OF 

CREDIT. 

T» 

No.  B  1450G.  NEW  YoRK)  June  ^  I881f 

GENTLEMEN  : — We  request  that  you  will  have  the  goodness  to 
furnish  ME.  EUGENE  HORTON,  the  bearer,  whose  signature  is  at 
foot,  with  any  funds  he  may  require  to  the  extent  of  £1000  (say 
One  Thousand  Pounds  Sterling),  against  his  drafts  upon  MESSRS. 
BROWN,  SHIPLEY  &  Co.,  London ;  each  draft  must  bear  the  num- 

T> 

ler  (No.  5  14506)  of  this  letter,  and  we  engage  that  the  same  shall 

meet  due  honor. 

Whatever  sums  MR.  HORTON  may  take  up,  you  will  please 
endorse  on  the  back  of  this  Circular  letter,  which  is  to  continue  in 
force  till  June  2,  188*2,  from  the  present  date,  June  2,  1881. 
We  are  respectfully,  gentlemen, 

Your  obedient  humble  servants, 

BROWN  BROTHERS  &  Co. 
The  Signature  of 

EUGENE  HORTON. 
To  MESSRS.  THE  BANKERS, 
Mentioned  on  the  third  page  of  this  Letter  of  Credit. 

42O.  The  following  draft,  drawn  by  the  issuer  of  the  letter  of 
credit  on  the  traveler's  American  representatives,  shows  the  expense 
connected  therewith  : 


No.  51931. 

£. 

s. 

d. 

Draft  dated  Lucerne,  July  20. 

25 

Commission  @  1^,    .... 

5 

T> 

fv        14-^ofi 

Interest  for  33  days  @  5^,      . 

2 

3 

25 

7 

3 

NEW  YORK,  Aug.  11,  1881. 
EXCHANGE  FOR  £25  7s.  3d. ,  at  $4^-  per  £  =  $122^, 

On  demand,  pay  this  FIRST  of  Exchange  (Second  unpaid),  to 
our  order,  the  sum  of  Twenty-five  Pounds  7/3  Sterling,  for  value 
received  by  MR.  EUGENE  HORTON. 

BPOWF  BROTHERS  &  Co. 
To  MESSRS.  G.  B.  HORTON  &  Co..  | 
New  York.  j 


FOREIGN   EXCHANGE. 


181 


NOTES. — 1.  The  commission  is  charged  only  on  amounts  drawn  and  not 
on  the  face  of  the  letter  of  credit. 

2.  The  interest  charged  is  calculated  to  cover  the  time  between  the  pay- 
ment of  the  original  draft  in  London  and  the  maturity  of  a  shortsight  remit- 
tance from  New  York  in  reimbursement. 

3.  Exchange  is  charged  at  the  current  rate  of  sight  exchange  on  London. 

421.  The  Intrinsic  Par  of  Exchange  is  the  value  of  the 
monetary  unit  of  one  country  expressed  in  that  of  another,  and  is 
based  on  the  comparative  fineness  and  weight  of  the  coins,  as 
determined  by  assay. 

The  intrinsic  par  of  exchange  between  different  countries  and  the  United 
States,  is  given  in  Art.  192. 

4:22.  The  Commercial  Par  of  Exchange  is  the  market 
value  in  one  country  of  the  coins  of  another. 

423.  The  Commercial  Rate  of  Exchange  is  the  market 
or  buying  and  selling  value  in  one  country  of  the  draffs  on  another. 

1.  In  giving  quotations  of  foreign  exchange,  no  reference  is  made  to  the 
par  value,  the  quotations  being  given  by  means  of  equivalents. 

2.  Premium  or  discount  for  exchange  can  not  long  exceed  the  transporta- 
tion charges  and  insurance  of  shipping  coin  ;  for,  if  a  merchant  can  ship  gold 
cheaper  than  he  can  buy  a  bill  of  exchange,  he  will  choose  the  former  method 
of  paying  his  indebtedness.     When  sight  exchange  is  4.84,  gold  can  be  im- 
ported at  a  small  profit ;   and  when  sight  exchange  is  4.89|,  gold  can  be 
exported  at  a  profit. 

424.  The  quotations  of  foreign  exchange,  Apr.  20,  1881,  were 
as  follows : 


Where  payable. 

60  days. 

Sight. 

London  : 
Prime  bankers'                                                     .      ... 

4  81| 

4  84 

Good  bankers'  and  prime  commercial 

4  81 

4  83i 

Documentary  commercial                              

4  78  J 

4  8H 

Cable  transfers                                                     4  84  > 

Paris  (francs)  

5.27-|- 

5.24f 

5.27| 

5.24»- 

Swiss  (francs)      

5.  26  J 

5.23^ 

Amsterdam  (guilders)  .           

.39| 

•39J 

Hambur°'  (reichsmarks)     .        .        .          

93| 

.941 

Frankfort  (reichsmarks)      .                                          ... 

93  £ 

.94| 

Bremen  (reichsmarks)  

.93| 

94| 

Berlin  (reichsmarks)         

.93| 

94J 

182  EXCHANGE. 

In  the  preceding  quotations,  exchange  is  below  par.  (See  intrinsic  par 
values  below,  or  in  Art.  192.)  When  exchange  is  above  par,  we  are 
exporters  of  gold ;  when  below  par,  we  are  importers  of  gold. 

425.  Exchange  on  England  (Sterling  exchange)  is  quoted  by 
giving  the  value  of  £1  in  dollars  and  cents. 

Thus,  when  exchange  is  4.84,  a  draft  of  £1  will  cost  $4.84 ;  of  £100,  $484. 
The  intrinsic  par  value  of  £1  is  $4.8665  (192). 

426.  Exchange    on    France,   Belgium,   and   Switzerland   is 
quoted  by  giving  the  value  of  $1  in  francs  and  centimes  (hun- 
dredths  of  a  franc). 

Thus,  when  exchange  is  5.27^,  $1  will  buy  a  bill  of  5  francs  and  27£ 
centimes;  a  draft  of  1000  francs  will  cost  $189.57  (1000  -J-  5.27-|).  The 
intrinsic  par  value  of  1  franc  is  19^  cents  (192) ;  of  the  equivalent  exchange, 
5.18|  (1.00 -5- .193). 

In  French,  Belgian,  and  Swiss  exchange,  the  higher  the  apparent  rate, 
the  less  the  value  of  the  draft.  Thus,  when  exchange  is  5.13,  a  draft  of  1000 
francs  is  worth  $194.93,  and  each  franc  is  worth  19TW  cents.  When  exchange 
is  5.26|,  the  same  draft  would  be  worth  $189.98,  and  each  franc  19  cents. 

427.  Exchange   on   Amsterdam  (Netherlands)  is  quoted  by 
giving  the  value  of  one  guilder  (gulden)  or  florin  in  U.  S.  cents. 

The  intrinsic  par  value  of  1  guilder  is  40T2<y  cents  (192). 

428.  Exchange  on  Germany  is  quoted  by  giving  the  value  of 
4  reichsmarks  in  cents. 

The  intrinsic  par  value  of  1  mark  is  23^  cents  (192) ;  of  4  marks 
95^  cents. 

429.  Documentary  Exchange  is  a  bill  drawn  by  a  shipper 
upon  his  consignee  against  merchandise  shipped,  accompanied  by 
the   bill   of   lading,   "to  order,"   and  the  insurance  certificates, 
covering  the  property  against  which  the  bill  is  draAvn. 

430.  Exchange  on  London  in  the  countries  named,  and  at 
London  on  the  same  countries,  is  quoted  as  follows  : 

United  States,  by  giving  the  value  of  £1  in  dollars  and  cents. 
France  and  Belgium,  by  giving  the  value  of  £1  in  francs  and  centimes. 
Germany,  by  giving  the  value  of  £1  in  marks  and  pfenniges. 
Austria,  by  giving  the  value  of  £1  in  florins  and  kreutzers. 
Netherlands,  by  giving  the  value  of  £1  in  guilders  and  cents. 
India,  by  giving  the  value  of  1  rupee  in  shillings  and  pence. 


EXAMPLES.  183 

EXAM  PLES. 

431.  1.  Find  the  cost  of  a  bill  of  exchange  on  London  for 
£225  at  4.81|. 

ANALYSIS.— If  £1  costs  $4.81f,  £225  will  cost  225  times  $4.81f. 

2.  What  is  the  value  of  a  draft  for  £324  16s.  at  4.87J? 

NOTE. — Write  one-half  of  the  greatest  even  number  of  shillings  as  tenths 
of  a  pound,  and  if  there  be  an  odd  shilling  write  5  hundredths.  Thus,  £324 
165.  =  £324.8  ;  £324  17s.  =  £324.85.  (See  Art.  2O4,  Ex.  7,  Note.)  The  value 
of  £324  16*.  at  4.87^  is  found  by  multiplying  $4.87£  by  324.8. 

3.  Find  the  value  of  a  draft  on  London  for  £379  12s.  7d.,  at 
4.1 


ANALYSIS. — If  each  penny  be  regarded  as  2  cents,  the 
result  will  be  sufficiently  accurate.  For  \\d.  the  maximum 
number  of  pence  in  any  example,  and  exchange  at  4.91,  the 
error  would  be  only  \  cent.  $4.86|  x  379.6  =  $1846.28. 
$1846.28  +  $0.14  -  $1846.42.  To  save  one  addition,  add  the 
14  cents  to  the  partial  products  as  in  the  operation. 

1846.420 

Find  the  value  of 

4.  £500  at  4.81f  8.  £512  13s.  at  4.84£. 

5.  £775  at  4.85J.  9.  £834  65.  6d.  at  4.88-g. 

6.  £837  at  4.83$.  10.  £675  Us.  Sd.  at  4.87$. 

7.  £84  85.  at  4.85.  11.  £225  7*.  5rf.  at  4.82f. 

12.  Find  the  cost  of  a  bill  of  exchange  on  Liverpool,  for  £875 
12s.  Gd.  at  the  par  value. 

13.  What  are  the  proceeds  of  a  draft  of  £959  5s.  4e?.,  sold 
through  a  broker,  at  4. 79 £,  brokerage  \%  ? 

14.  An  exporter  sold  a  draft  for  £540  3s.  on  Manchester,  pay- 
able in  London,  at  4.84,brokerage  \%.    What  were  the  proceeds  ? 

15.  Find  the  proceeds  of  a  draft  on  Newcastle-on-Tyne,  at  60 
days'  sight  for  £1764  15s.,  payable  in  London,  at  4.82,  brokerage 
on  exchange  \%. 

16.  An  importer  purchased  a  bill  of  exchange  on  London,  at  3 
days'  sight,  for  £488  16s.  6d.,  at  4.85J.     What  was  the  cost? 


184  EXCHANGE. 

17.  How  much  exchange  on  London  at4.81|  will  $821.99  buy  ? 

ANALYSIS. — $4.81f  will  buy  exchange  for  £1 ;  hence,  $821.99  will  buy  as 
many  pounds  as  $4.81  f-  are  contained  in  $821.99,  or  £170.625.  £170.625 
=  £170  12*.  6<Z. 

18.  What  will  be  the  face  of  a  3  days'  bill  of  exchange  on 
London  that  can  be  bought  for  $5964.13,  exchange  4.86J  ? 

19.  The  face  of  a  bill  of  exchange  was  £875,  and  its  cost  was 
$4233.91.     What  was  the  rate  of  exchange  ? 

20.  An  exporter  received  $9063.22  for  a  bill  of  exchange  that 
was  sold  through  a  banker  at  $4.86 J ;  what  was  the  face  of  the 
bill,  the  broker's  commission  being  %%  ? 

21.  Find  the  cost  of  a  bill  of  exchange  on  Paris  for  7000  francs 
at  5.211. 

OPERATION. 

5. 21-3- )     7000  ANALYSIS. — Since    5.21|    francs  cost    $1, 

n  Q  7000    francs    will    cost    as    many  dollars    as 

5.21^  francs  are  contained  times  in  7000  francs. 


41.75    )  56000. 0000  ( 

Find  the  value  of 

22.  6000  francs  at  5.16.  25.  8475  francs  at  5. 19$. 

23.  5000  francs  at  5. 18$.  26.  7216  francs  at  5.17}. 

24.  4000  francs  at  5. 21|.  27.  987.60  francs  at  5. 2QJ. 

28.  Find  the  cost  of  a  draft  on  Antwerp  at  3  days'  sight,  for 
9640  francs,  at  5.1 9f. 

29.  What  is  the  value  of  a  draft  on  London  for  £416  16s.  3d., 
at  4.85|  ? 

80.  Bought  exchange  on  Geneva,  through  a  broker,  for 
8000  francs  at  60  days'  sight ;  what  was  the  cost  of  the  draft, 
exchange  being  5.20f,  brokerage  $^? 

31.  What  is  the  cost  of  a  draft  on  Paris  for  12420  francs,  at 
6.19},  brokerage  on  exchange  $$? 

32.  What  will  it  cost  to  remit  to  Antwerp  8750  francs  at  the 
par  value  ? 

33.  Sold  through  a  broker  a  draft  on  Geneva  for  7324  francs. 
What  were  the  proceeds,  exchange  being  5.1 8-f,  brokerage  \%  ? 

84.  What  will  be  the  face  of  a  bill  of  exchange  on  Geneva  that 
can  be  bought  for  $15372,  exchange  selling  at  5.22$  ? 

35.  Paid  for  a  draft  on  Paris  $3460.32 ;  what  was  the  face  of 
the  draft,  exchange  being  5.19-jj,  and  brokerage  \%  ? 


EXAMPLES.  185 

36.  A  merchant  paid  $6272  for  a  bill  of  exchange  of  32512.48 
francs  ;  what  was  the  rate  of  exchange  ? 

87.  Find  the  cost  of  a  bill  of  exchange  on  Hamburg  for 
14400  marks  (Reichsmarks)  at  94J-. 

OPERATION. 

4  )  14400 

rr:::  ANALYSIS.—  Since  4  marks  cost  $0.94£,  14400  marks  will 

cost  3600  (14400  -*-  4)  times  $0.94|,  or  $3388.50. 


3388.50 

Find  the  value  of 

88.  7200  marks  at  94.  41.  1237  marks  at  93}. 

89.  8416  marks  at  93J.  42.  9894  marks  at  95}. 
40.  3456  marks  at  95}.  48.  6515  marks  at  94J. 

44*  What  is  the  cost  of  a  bill  of  exchange  on  Frankfort  for 
16200  marks  at  95£? 

45.  Sold  a  bill  of  exchange  on  Hamburg  for  13200  marks,  at 
94}  ;  what  was  the  amount  received,  brokerage  \%  ? 

46.  An  importer  purchased  a  bill  of  exchange  on  London  for 
£318  105.  7£,  at  4.85|  ;  what  did  it  cost  ? 

47.  What  were  the  proceeds  of  a  draft,  sold  through  a  broker, 
for  8748  marks,  at  94},  brokerage  \%  ? 

48.  An  exporter  sold  a  draft  on  Paris  for  12275  francs,  at 
5.19}  ;  what  were  the  proceeds,  brokerage  \%  ? 

49.  What  is  the  face  of  a  bill  on  Hamburg  that  cost  $816, 
exchange  94£  ? 

ANALYSIS.—  Since  $.94£  will  buy  4  marks,  $816  will  buy  4  times  as  many 
marks  as  $0.94£  is  contained  times  in  $816. 

50.  What  is  the  face  of  a  3  days'  draft  on  Bremen,  that  was 
purchased  in  New  York  for  $3261.60,  exchange  94$-  ? 

51.  The  cost  of  a  draft  of  12320  marks  was  $2922.15  ;  what 
was  the  rate  of  exchange  ? 

52.  Find  the  cost  of  a  bill  of  exchange  on  Amsterdam,  for 
7240  guilders,  at  40}. 

53.  Find  the  cost  of  a  bill  of  exchange  on  Amsterdam,  at 
60  days'  sight,  for  12480  guilders,  exchange  39},  brokerage  \%. 

54.  An  exporter  received  $1890,86  for  a  bill  of  exchange  on 
Amsterdam;  what  was  its  face,  exchange  being  41-J-,  brokerage 

it? 


186  EXCHANGE. 

55.  At  40-f,  how  much  exchange  on  Amsterdam  will  $2877.93 
buy? 

56.  The  value  of  a  draft  of  5280  guilders  is  $2145  ;  what  is 
the  quotation  ? 

57.  The  dividends  of  the  N.  Y.  0.  and  H.  K.  E.  Co.,  are  paid 
in  London  at  the  rate  of  49-J-  pence  to  the  dollar.     What  is  the 
equivalent  rate  of  exchange  ? 

58.  Find  the  value  in  U.  S.  money  of  16319  bushels  of  wheat 
at  45.  tyd.  per  bushel,  exchange  4.86  J. 

59.  A  merchant  sent  a  messenger  with  a  bill  of  exchange  of 
20000  francs  to  two  bankers,  A  and  B,  with  instructions  to  sell  it 
to  the  best  advantage.     A  offered  5.27  and  B  5.27^.     The  messen- 
ger imprudently  accepted  the  latter  offer.     How  much  did  the 
merchant  lose  by  the  ignorance  of  the  messenger  ? 

60.  When  United  States  4  per  cent,  consols  are  quoted  in  New 
York  at  114£,  and  sterling  exchange  at  4.83J,  what  should  be  the 
London  quotation  of  the  bonds  ?    What  should  be  the  London  quo- 
tation of  4-J  per  cent,  bonds,  the  New  York  quotation  being  113  J  ? 

NOTE. — In  London,  all  American  securities  are  quoted  on  an  assumed 
value  of  the  pound  sterling  of  $5,  instead  of  the  actual  value  of  $4.8665,  or, 
more  definitely  speaking,  its  commercial  value  determined  by  the  rate  of 
exchange.  Multiplying  the  New  York  quotation  by  5  and  dividing  by  the 
rate  of  exchange,  the  result  will  be  the  equivalent  London  quotation. 

61.  When  American  railway  stocks  are  quoted  in  London  at 
88,  what  is  the  equivalent  New  York  quotation,  sterling  exchange 
being  quoted  in  New  York  at  4.88£  ? 

62.  What  is  the  London  equivalent  of  a  New  York  quotation 
of  142,  exchange  being  4.83  ? 

63.  At  Paris,  what  is  the  value  of  a  draft  on  London  of  £550, 
exchange  being  25.36J? 

64.  At  London,  what  is  the  cost  of  a  draft  on  Hamburg  of 
8000  marks,  exchange  being  20.45? 

65.  At  Vienna,  what  is  the  cost  of  a  draft  on  London  of  £625, 
exchange  being  11.75  ? 

66.  At  London,  what  is  the  value  of  a  draft  on  Calcutta  of 
12000  rupees,  exchange  being  quoted  at  Is.  8-fad.  ? 

67.  A   commission   merchant  wishes  to  remit   $2475  to  his 
principal  in  England.     How  large  a  draft  must  he  purchase, 
exchange  being  4.83 J  ? 


EQUATION    OF    ACCOUNTS. 


DEFINITIONS. 

432.  Equation  of  Accounts  (called  also  Equation  of  Pay- 
ments and  Averaging  Accounts)  is  the  process  of  finding  the  time 
when  several  debts  due  at  different  dates  may  be  paid  in  one 
amount  without  loss  of  interest  to  either  party.     It  is  also  the 
process  of  finding  the  time  when  the  balance  of  an  account  having 
both  debits  and  credits  may  be  paid  without  loss  of  interest  to 
either  party.     This  time  is  called  the  equated  or  average  time. 

433.  To  find  the  equated  time  when  the  items  of  the 
account  are  all  on  the  same  side,  i.  e.,  all  debits  or  all 
credits. 

ANALYTICAL  STEPS. — By  assuming  a  certain  date  as  the  time  of  settle- 
ment, we  find  what  the  loss  or  gain  of  interest  would  be  to  the  payer  if  all 
the  bills  were  paid  by  him  on  that  date.  We  next  find  in  how  many  days  the 
total  amount  of  the  bills  would  produce  a  sum  equivalent  to  this  loss  or  gain  of 
interest,  and  find  the  true  day  of  settlement  by  counting  forward  or  back- 
ward this  number  of  days  from  the  assumed  date.  Thus,  if  the  sum  of  the 
several  bills  is  $1000,  and  the  loss  of  interest  to  the  payer  at  the  assumed 
date  of  settlement  is  $10  (the  interest  of  $1000  at  60  days  at  6%),  it  is  evident 
that  the  true  date  of  settlement,  or  the  time  when  there  would  be  no  loss  of 
interest  to  either  party,  must  be  60  days  after  the  assumed  date. 

NOTES. — 1.  The  interest  on  the  bills  paid  after  they  became  due  would 
equal  the  interest  on  the  bills  paid  in  advance,  the  former  being  a  gain  to  the 
payer,  and  the  latter,  a  loss. 

2.  Any  date  may  be  assumed  as  the  time  of  settlement.  For  convenience, 
the  earliest  or  latest  date  is  generally  used.  If  the  earliest  date  is  taken,  the 
estimated  interest  is  a  loss  to  the  payer ;  if  the  latest  is  taken,  the  interest  is 
a  gain. 


188  EQUATION    OF   ACCOUNTS. 

When  the  time  is  found  by  Compound  Subtraction,  or  each  month  is 
regarded  as  30  days,  the  last  day  of  the  month  preceding  the  earliest  item  is 
the  most  convenient.  (See  second  interest  method.) 

In  Equation  Tables,  Dec.  31  or  Jan.  1  is  taken  for  all  examples. 

The  assumed  date  is  sometimes  called  the  focal  date. 

3.  Any  rate  of  interest  may  be  used  in  making  the  computations,  6  and 
12  being  the  most  convenient  rates. 

434.  Ex.  At  what  date  may  the  following  bills  of  merchan- 
dise be  paid  in  one  amount  without  loss  of  interest  to  either 
party?  Due  Apr.  10,  $114;  due  Apr.  26,  $140;  due  May  22, 
$320 ;  due  June  6,  $976. 

OPERATION. — PRODUCT  METHOD. 

Due  Apr.  10,     $114  x     0  =          0 

"     26,       140  x  16  =    2240 

"     May  22,       320  x  42  =  13440 

"    June  6,       976  x  57  =  55632 

1550  )  71312  (  46  days 

after  Apr.  10,  or  May  26. 

ANALYSIS. — For  convenience,  assume  Apr.  10,  the  earliest  due  date,  as 
the  time  of  settlement.  If  the  first  bill,  which  is  due  Apr.  10,  is  paid  on  that 
date,  there  will  be  no  loss  or  gain  of  interest  to  either  party.  If  the  second 
bill,  which  is  due  Apr.  26,  is  paid  Apr.  10,  16  days  before  it  is  due,  there  will 
be  a  loss  to  the  payer  of  the  interest  or  the  use  of  $140  for  16  days,  or  $2240  for 
1  day.  On  the  third  bill,  there  will  be  a  loss  of  the  interest  of  $320  for 
42  days,  or  $13440  for  1  day.  On  the  fourth  bill,  there  will  be  a  loss  of  the 
interest  of  $976  for  57  days,  or  $55632  for  1  day.  If  all  the  bills  are  paid 
Apr.  10,  there  will  be  a  loss  to  the  payer  of  the  interest  of  $71312  for  1  day, 
or  of  $1550  for  46  days.  Since  the  loss  of  interest  to  the  payer  is  equivalent 
to  the  interest  of  the  total  amount  of  the  bills  for  46  days,  it  is  evident  that 
the  day  when  there  would  be  no  loss  of  interest  must  be  46  days  after 
Apr.  10,  or  May  26.  The  payer  is  entitled  to  defer  payment  46  days  after  the 
assumed  date  as  a  compensation  for  the  estimated  loss. 

The  gain  of  interest  to  the  payer  on  the  first  three  bills,  which  are  paid 
after  they  are  due,  equals  the  loss  of  interest  on  the  fourth  bill,  which  is  paid 

before  it  is  due. 

PROOF. 

The  interest  of  $114  for  46  days  at  6^  is  .     .     .     .     .     .     $0.874 

"          "      "    140  "   30     "          " 70 

"      "    320  "     4     "          " .213 

Total  gain  of  interest  to  the  payer        1.787 

The  interest  (a  loss  to  the  payer)  of  $976  for  11  days  is  .       1.789 


EQUATION    OF   ACCOUNTS.  189 

NOTES. — 1.  In  finding  the  number  of  days  from  the  assumed  date  to  the 
other  dates,  instead  of  calculating  from  the  assumed  date  each  time,  find  the 
interval  from  one  date  to  the  next  and  add  it  to  the  last  number  of  days. 
Thus,  from  Apr.  10  to  May  22  is  42  days,  and  from  May  22  to  June  6,  15  days ; 
hence,  from  Apr.  10  to  June  6  is  57  (42  +  15)  days.  (See  Art.  21O,  Ex.  3.) 

2.  To  determine  the  due  date,  find  the  number  of  days  in  the  operation 
nearest  to  the  quotient,  and  add  or  subtract,  as  may  be  necessary,  the  differ- 
ence between  it  and  the  quotient,  to  its  corresponding  date.     Thus,  in  the 
above  example,  the  number  of  days  in  the  operation  nearest  to  the  quotient  is 
42  ;  hence  the  due  date  is  4  (46-42)  days  after  May  22,  or  May  26.     (See  Art. 
254,  Ex.  3.) 

3.  If  the  fraction  of  the  quotient  is  less  than  |,  disregard  it;  if  more  than 
\,  add  1  day  to  the  integral  number  of  days  in  the  quotient. 

435.  KULE    FOR    THE    PRODUCT    METHOD.  —  Assume    the 
earliest  due  date  as  the  day  of  settlement  for  all  the  items. 
Multiply  each  item  by  the  number  of  days  intervening 
between  the  assumed  date  of  settlement  and  the  date  of  the 
item ;  and  divide  the  sum  of  the  several  products  by  the 
sum  of  the  account.     Count  forward  from  the  assumed  date 
the  number  of  days  obtained  in  the  quotient.     The  result 
will  be  the  equated  time. 

436,  OPERATION. — FIRST  INTEREST  METHOD. 

Days.  Interest. 


Due 

Apr. 

10, 

$114 

0 

$.00 

a 

n 

26, 

140 

16 

i 

.233 

.14 

for 
ft 

10 
6 

days. 

a 

( 

1. 

60 

a 

30 

tt 

" 

May 

99 

/&/£, 

320 

42 

i 

64 

tt 

12 

« 

(4.88 

tt 

30 

" 

" 

June 

6, 

976 

57 

•<  2.44     " 

15 

" 

60) 

15.50 

( 

1. 

952 

" 

12 

" 

"7258 

ill. 

885 

(  46  days 

after  Apr.  10,  or  May  26. 

ANALYSIS.— Assume  Apr.  10,  the  earliest  due  date,  as  the  time  of  settle- 
ment. If  the  total  amount  ($1550)  of  the  bills  is  paid  Apr.  10,  the  assumed  date 
of  settlement,  there  will  be  a  loss  of  interest  to  the  payer  of  $11.885.  The 
interest  of  $1550  for  60  days  at  6  #  is  $15.50,  and  for  1  day,  $0.258.  It  will 
take  $1550  to  produce  $11.885  interest  as  many  days  as  $0.258  is  contained 
times  in  $11.885,  or  46  days.  If,  at  the  assumed  date  of  settlement,  there  is  a 
loss  to  the  payer  of  the  interest  of  $1550  for  46  days,  the  true  day  of  settle- 
ment must  be  46  days  later,  or  May  26. 


190  EQUATION  OF  ACCOUNTS. 

437.  OPERATION.  —  SECOND  INTEREST  METHOD. 


Mo.  Days.  Interest. 

0     Apr.  10,     $114       $0.19 


for  30  day, 


0  «     26,       140    {      -Jf  I      6     „ 

(    1.60  "      I  mo. 

1  May  22,      320    \    1.067  "  20  days. 

.107  "      2     " 


2    June    6,      976 
2)IK50 


(    9.76      « 
\      .976    « 


7.75    )  14.306  ( 1  mo.  25  da.  after  Mar.  31, 
7.75  or  May  25. 

6.556 

30 

7.75)196.680(25  days. 
1550 

4168 

3875 

293 

ANALYSIS. — By  this  method,  the  last  day  of  the  month  preceding  the 
earliest  due  date  is  assumed  as  the  date  of  settlement,  and  the  time  is  iound 
by  Compound  Subtraction,  each  month  being  regarded  as  80  days. 

The  months  are  placed  on  the  margin  and  the  days  correspond  with  the 
number  of  days  in  the  given  dates. 

Mar.  31,  the  assumed  day  of  settlement,  there  is  a  loss  to  the  payer  of 
$14.306  interest,  or  the  interest  of  $1550  for  1  mo.  25  da.  The  equated  time 
is  therefore  1  mo.  25  da.  after  Mar.  31,  or  May  25. 

Since  this  method  regards  all  months  as  30  days  each,  its  results  are  not 
strictly  accurate.  The  error  in  this  example  is  1  day.  (See  preceding  results.) 

When  this  method  is  used,  and  accurate  results  are  required,  the 
necessary  corrections  may  be  made  by  adding  to  the  intervals  of  time  1  day 
for  each  intervening  month  containing  31  days.  If  the  month  of  February  is 
included,  2  days  should  be  subtracted  in  a  common  year  and  1  day  in  a  leap 
year. 

In  counting  forward  to  find  the  equated  time,  the  opposite  correction 
should  be  made.  Thus,  if  the  assumed  date  is  June  30  and  the  quotient  is 
2  mo.  20  da.,  the  equated  time  would  be  Sept.  18,  2  days  being  subtracted  for 
July  and  August. 

The  following  is  the  corrected  operation  for  the  given  example,  1  day 
being  added  to  the  time  of  the  fourth  item  for  the  month  of  May.  The  result 
is  the  same  as  by  the  product  and  the  first  interest  methods. 


EQUATION    OF   ACCOUNTS.  191 


Mo. 

Days. 

OPERATION. 

Interest. 

0 

Apr. 

10, 

$114 

$0.19 

0 

tf 

26, 

140 

(      .466  for 
\      .14      " 

20 
6 

days. 

tt 

(    1.60      " 

1 

mo. 

1 

May 

22, 

320 

1.067    " 

20 

days. 

(      .107    " 

2 

" 

(    9.76      " 

2 

mo. 

2 

June 

6  +  1 

,     976 

•j      .976    " 

6 

days. 

2 

)  "16.50 

(      .162    " 

1 

tt 

7.75    )  14. 468(1  mo. 26  Rafter  Mar.  31, 
7.75  or  May  26. 

6.718 

J30 

7.75)  201. 540  (26  days. 

EXAM  PLES. 

438.  1.  At  what  date  may  the  following  bills  be  paid  in  one 
amount  without  loss  of  interest  to  either  party  ?  Due  Sept.  10, 
$145;  Sept.  28,  $144;  Oct.  8,  $75  ;  Oct.  23,  $512. 

2.  What  is  the  equated  time  for  the  payment  of  the  following 
bills?    Due  Mar.  28,  $446;  May  3,   $212;  May  15,  $116;  May 
31,  $475  ;  June  12,  $345. 

3.  What  is  the  average  due  date  of  the  following  bills,  each 
being  due  at  the  date  given?    Jan.  5,  $127.85  ;  Jan.  26,  $134.18  ; 
Feb.  5,  $249.40  ;  Feb.  23,  $418.73  ;  Feb.  28,  $176.25. 

NOTE.— The  result  will  be  practically  the  same  if  the  nearest  dollar  is 
used  in  multiplying  or  in  calculating  the  interest.  Thus,  in  the  above 
example,  regard  the  amounts  as  128,  134,  249,  419,  and  176  respectively. 

When  there  are  several  items  in  the  example,  some  accountants  omit  the 
cents  and  units  of  dollars,  and  use  the  nearest  number  of  tens.  Thus,  if  the 
above  account  were  of  sufficient  length,  the  numbers  might  be  regarded  as 
13,  13,  25,  42,  and  18  respectively.  In  this  example  the  result  is  the  same, 
but  in  some  examples,  containing  the  same  number  of  items,  there  would  be 
a  discrepancy  of  one  or  more  days. 

4.  Sold  a  customer  bills  at  the  due  dates  and  to  the  amounts 
specified  :  June  1,  $152.73  ;  June  15,  $114.28 ;  July  16,  $247.84 ; 
July  25,  $88.90  ;  Aug.  18,  $735.42  ;  Aug.  29,  $416.34.     When  may 
the  whole  indebtedness  be  equitably  discharged  at  one  payment  ? 


192 


EQUATION    OF  ACCOUNTS. 


5.  Average  the  following  account : 

NEW  YORK,  July  1,  1882. 

To  LORD  &  TAYLOR,  Dr. 


MESSRS.  RICE,  STIX  &  Co., 


1882. 

Apr.     4 

Mdse.  30  days  per  bill  rendered.      .     . 

1816 

37 

"      21 

"     30     "        "            "              .     . 

724 

25 

May  13 

((         3Q        «               «                     tt                         ^ 

342 

46 

"      25 

"     30     "         "            " 

535 

84 

June  16 

"     30     "        "            "              . 

.628 

62 

Due  by  equation  June  *,  1882. 

**** 

** 

NOTE. — When  several  bills  are  sold  on  a  common  term  of  credit,  first 
find  the  average  date  of  purchase,  and  to  the  result  add  the  common  term  of 
credit. 

Certain  merchants  sell  uniformly  on  the  same  term  of  credit,  while  others 
sell  on  different  credits,  depending  upon  the  class  of  goods,  the  standing  of 
the  customer,  the  state  of  the  market,  etc.  (See  Art.  275.) 

6.  A.  Hamilton  bought  of  F.  A.  Leggett  &  Co.,  several  bills  of 
goods,  as  follows : 

May  16,  a  bill  of  $212.46  on  60  days'  credit. 

"     28,        "         318.40  "  60 

June    6,        "         275.64  "  60 

"   21,        "         187.83   "  60 

July  13,        "         835.60   "  60 

A  60-day  note  for  the  whole  amount  is  given  in  settlement. 
What  must  be  its  date,  no  allowance  being  made  for  the  days  of 
grace  ? 

7.  Sold  on  a  credit  of  90  days  the  following  bills  of  goods : 
Mar.   4,  $194.13;   Mar.   27,  $222.36;  Apr.   12,  $538.72;  May  3, 
$432.64;  May  28,  $303.10.     What  is  the  equated  time  of  pay- 
ment ?    How  much  will  settle  the  account  Aug.  1,  at  6%  ?     How 
much  July  1  ? 

NOTE. — When  monthly  statements  are  sent  to  customers  the  accounts 
are  frequently  averaged.  (See  Ex.  5.)  When  the  account  is  averaged,  the 
simplest  method  of  finding  the  cash  balance  due  at  a  certain  date,  is  to  cal- 
culate the  interest  on  the  total  amount  from  the  average  date  to  the  time  of 
payment,  and  add  it,  if  the  time  of  settlement  is  after  the  average  date,  and 
subtract  it,  if  before. 


EQUATION    OF  ACCOUNT'S.  193 

Since  a  fraction  of  a  day  is  not  considered  in  determining  the  average 
date,  this  method  of  finding  the  cash  balance  is  not  as  accurate  as  that  of 
Art.  453,  in  which  the  interest  is  reckoned  on  each  item  separately. 

8.  A  commission  merchant  sold  several  bills  of  goods,  on  a 
credit  of  4  months,  as  follows  :    Aug.  16,  1881,  $387 ;  Sept.  4, 
1881,  $243.60;  Sept.  18,  1881,  $637.75;  Oct.  28,  1881,  $165.50; 
Dec.  10,  1881,  $856.45.    What  is  the  equated  time  of  payment  ? 

NOTE. — The  above  account  may  be  averaged  by  first  finding  the  average 
date  of  purchase,  and  adding  the  common  term  of  credit ;  or  by  finding  the 
due  date  of  each  bill  separately,  and  determining  the  average  due  date  from 
the  dates  thus  found.  Since  the  months  have  not  uniformly  the  same  num- 
ber of  days,  the  results  by  the  two  methods  sometimes  differ  by  one  or  more 
days,  when  the  common  term  of  credit  is  expressed  in  months. 

9.  Bought  goods  on  6  months'  credit  as  follows  :    Feb.  16, 
1881,  $376.50;  Mar.  12,  1881,  $287.40;  Mar.  19,  1881,  $612.87; 
Apr.  5,  1881,  $345.60;   Apr.  26,  1881,  $134.80;   June  1,  1881, 
$612.35.     What  is  the  average  time  of  maturity  ?    How  much 
would  balance  the  account  Jan.  1, 1882  ?     How  much  Oct.  1, 1881  ? 

10.  Park  and  Tilford  sold  to  R.  M.  Bishop  &  Co.  the  following 
bills  of  merchandise  on  60  days'  credit:     Feb.  24,  $176.82;  Feb. 
28,  $327.49;  Mar.  16,  $282.75;  Mar.  28,  $512.14;  Apr.  7,  $438.36; 
Apr.  14,  $109.70  ;  May  1,  $632.65.     What  is  the  equated  time  of 
payment,  and  how  much  would  be  required  to  balance  the  account 
June  1  ?     How  much  July  1? 

11.  The  following  bills  of  merchandise  were  purchased  on  4 
months'  credit:    June  1,  $237.16;  June  18,  $146.75;  June  30, 
$333.84  ;  July  5,  $416;  July  16,  $535.62  ;  July  27,  $912.33  ;  Aug. 
13,  $345.60.     A  note  payable  in  4  months  was  given  in  settlement. 
What  was  its  date,  no  allowance   being  made  for  the  days  of 
grace  ? 

12.  Bought  goods  on  60  days'  credit  as  follows:     Aug.  11, 
$487.60  ;  Aug.  20,  $398.30  ;   Sept.  1,  $411.26  ;   Sept.  13,  $283.36  ; 
Sept.  22,  $112.43  ;    Sept.  30,  $555.55  ;    Oct.  20,  $342.48  ;    Nov.  4, 
$337.64.     What  is  the  average  due  date  ? 

13.  What  is  the  average  time  for  the  payment  of  the  following 
bills,  each  being  sold  on  a  credit  of  4  months  ?    Feb.  29,  $224.37; 
Mar.  13,  $642.50;   Mar.  31,  $377.65;   May  4,  $510.10;    May  19, 
$388.84;  June  3,  $476.25  ;  June  19,  $227.30 ;  June  30,  $562.75. 

13 


194  EQUATION    OF  ACCOUNTS. 

14-  Bought  several  bills  of  goods  as  stated  below  : 

June    3,  a  bill  of  $375  on  30  days'   credit. 

"  28,  "  420  "  60  "  " 
July  16,  "  560  "  4  months'" 
Sept  4,  "  228  "  90  days'  " 

What  is  the  equated  time  of  payment  ? 

NOTE. — When  the  bills  are  sold  on  different  terms  of  credit,  first  find  the 
due  date  of  each  bill  separately  as  in  the  following  operation. 

OPERATION. — PRODUCT  METHOD. 

Date  of  purchase.     Credit.  Due  date.       Amount.      Days.         Products. 

June  3,   30  days,  July  3,  $375  x   0  =     0 

"  28,   60  "   Aug.  27,   420  x  55  =  ***** 

July  16,   4  mo.,   Nov.  16,   560  x  ***  =  ***** 

Sept.  4,   90  days,  Dec.  3,   228  x  ***  —  ***** 

****  ******  ** 


OPERATION.— APPROXIMATE  INTEREST  METHOD.* 

Mo.  Days.  Credit.  Interest. 

0    June    3,     $375,     30  days,    I  ^ '«'    \T 

(      .187    "      3  days. 

(    4.20      "      2  mo. 

0  "      28,       420,     60      "  1.68      "    24  days. 

(      .28      "      4     " 
11.20      "      4:  mo. 

1  July  16,       560,       4  mo.,      J    2-80     "      X    " 

.933    "    10  days. 

.56      "      6     " 

3    ^    42)i|t     90dayS'^::     ^ 

7.915          7.915  )  30.708  (  3  mo.  26  da.  after 
23.745     May  31,  or  Sept.  26. 
6.963 

30 

7. 915)  208.890  (26  days. 

*  See  second  interest  method,  Art.  437. 


EQUATION    OF  ACCOUNTS.  195 

45.  What  is  the  equated  time  for  the  payment  of  the  following 
bills  ? 

July     5,  1882,  $516.60  on    4  months'  credit. 

28,     "        327.35    "  60  days7  " 

Aug.  15,     "        147.84   "     4  months'      " 

Sept.     8,     "       485.42    "  30  days'  " 

"      25,     "        230.39    "  60     "  « 

16.  Sold  several  bills  of  goods  as  follows : 

May     4,  a  bill  of  $418.75  on  30  days'  credit. 

"     16,  «           322.86    "  60     " 

June    1,  "           513.44    "  4  months' " 

"     12,  "           118.70    «  60  days'       " 

"     30,  "           786.30    "  6  months'  " 

July  16,  "           274.85    «  60  days'       « 

"What  is  the  average  time  of  payment,  and  how  much  would 
balance  the  account  Sept.  1  ?    How  much  Oct.  1  ? 

17.  What  is  the  average  time  of  maturity  for  the  payment  of 
the  following  bills  ? 

Mar.     4,  1883,  $117.26  on    4  months'  credit. 


"      21,     " 

97.43   " 

30  days' 

" 

"      29,     " 

243.84   « 

60   ." 

U 

Apr.    16,    " 

376.14   " 

4  months' 

« 

"      30,     " 

182.75    « 

90  days' 

tt 

May   18,    " 

412.50   « 

60     " 

tt 

June     1,     " 

518.65   « 

30     " 

te 

18.  Bought  goods  of  Henry  Welsh  as  follows  : 

Nov.  13,  1881,  a  bill  of  $138.42  on  30  days'  credit. 


tt 

30,     " 

" 

416.10 

te 

60 

tt 

" 

Dec. 

16,     « 

r« 

324.70 

" 

30 

" 

a 

Jan. 

5,  1882, 

r< 

586.85 

" 

4 

months' 

te 

tt 

26,     " 

(f 

234.38 

" 

60 

days' 

ee 

Feb. 

12,     " 

ttf 

93.60 

tt 

4 

months' 

ee 

f* 

23,     « 

r< 

618.75 

(t 

30 

days' 

a 

Mar. 

5      " 

tt 

374.36 

tt 

60 

tt 

ee 

What  is  the  equated  time  for  the  payment  of  the  whole? 


196  EQUATION    OF  ACCOUNTS. 

19.  A  commission  merchant  made  the  following  sales  for  a 
consignor  : 

May  10,  $175,  on  a  credit  of  4  months,  or  30  days  less  5%. 

"     18,    243,  "          4       "  30     " 

"    31,    364,  "  4       "  30     " 

June  18,    387,  "  4       "  30     " 

July    1,    216,  "          4       "  30     " 

What  is  the  average  due  date  ? 

NOTE. — Since  each  of  the  above  bills  was  sold  on  two  different  terms  of 
credit,  the  account  may  be  averaged  on  two  different  bases  producing  different 
results.  The  average  date  of  purchase  is  June  5.  If  the  account  is  settled 
on  the  first  term  of  credit,  the  total  amount  of  the  bills,  $1385,  will  be  due  4 
months  after  June  5,  or  Oct.  5.  If  the  account  is  settled  on  the  second  term 
of  credit,  there  will  be  $1315.75  ($1385  less  5  % )  due  30  days  after  June  5,  or 
July  5.  Since  money  is  always  worth  less  than  20 %  (4x5^),  the  second 
method  is  in  favor  of  the  commission  merchant.  Probably  most  of  his  buyers 
settle  their  bills  on  the  second  terms,  and  thus  take  advantage  of  the  discount. 

20.  Average  the  following  account  on  both  terms  of  credit : 

Jan.  16,  $387.65  on  6  months'  credit  less  4%  30  days. 

"  28,  117.42  "  6  "  "  30  " 

Mar.  1,  482.60  "  6  "  "  30  " 

"  13,  618.32  "  6  "  "  30  " 

Apr.  4,  291.50  "  6  "  "  30  " 

"      11,  433.75  "  6  "  "  30  " 

"      23,  877.42  "  6  "  "  30  " 

21.  A  commission  merchant  made  the  following  sales  :    Aug. 
1,  1881,  $387.40  ;  Aug.  10,  1881,  $416.75  ;  Sept.  5, 1881,  $583.28; 
Sept.  20,  1881,  $144.13;   Oct.  3,  1881,  $582.76;  Oct.  24,  1881, 
$327.41.     What  is  the  net  amount  and  the  average  due  date  if  the 
goods  were  sold  on  the  following  time  ?    "  60  days,  or  2%  discount 
if  paid  in  10  days." 

22.  A  commission  merchant  sold  the  bills  mentioned  below  on 
the  following  terms  :     Net  60  days,  or  \%  discount  in  30  days,  or 
2%  discount  in  10  days.     Apr.  19,  $327.85;  May  1,  $282.64  ;  May 
13,   $117.49;    June    18,   $486.40;    June    30,   $380.36;    July  10, 
$516.64;  July  17,  $222.27.  t  What  is  the  net  amount  and  the  due 
date  on  each  term  of  credit  ? 


EQUATION    OF  ACCOUNTS.  197 

23.  Average  the  following  sales  made  by  a  commission  merchant 
for  a  consignor : 

Mar.  18,  $428.32  on    4  months'  credit,  or  30  days  less  $%. 

"     31,     385.74   "   60  days'  " 

Apr.     5,     212.50    "     4  months'      "  "  " 

"      26,     678.34   "   30  days' 
May   10,     824.60    "     4  months'      " 

NOTE. — If  the  1st,  3rd,  and  5th  items  are  settled  on  the  basis  of  4  months' 
credit,  the  operation  would  be  as  follows  by  the  product  method : 


OPERATION. 


Due  July  18,  $428.32  x  53  =  22684 
«  May  30,  385.74  x  4  =  1544 
"  Aug.  5,  212.50  x  71  =  ***** 
"  May  26,  678.34  x  0  =  0 

"    Sept.  10,  _82460  x  107  =    ***** 

2529.50  )  ******  (  ** 

after  May  26. 

NOTE. — If  the  1st,  3rd,  and  5th  items  are  settled  on  a  credit  of  30  days 
less  5  % ,  the  operation  would  be  as  follows : 

OPERATION. 

Due  Apr.  17,  $428.32  x    0  =          0 

«    May     5,     212.50  x  18  =    3816 

«    June    9,     824.60  x  53  =  43725 

1465.42  47541 

Less  5%        73.27  _2377 

1392.15  45164 

"    May    30,     385.74  x  43  =  ***** 

"       "      26,     678.34  x  39  =  ***** 

2456.23  )  *****  (  **  days 

after  Apr.  17. 

24.  Find  the  average  time  for  the  payment  of  the  following  sales : 

Mar.  16,  $874.42  on  30  days'  credit. 

"  31,  555.37  "  60     «  " 

Apr.  5,  677.30  "  60     "  " 

"  16,  426.76  "  30     "  " 

"  24,  388.65  "  4  months'   "        or  30  days  less  5  fa 

May  3,  112.60  "  4       «  "         «  30    «      "   5 fa 

"  10,  989.10  "  60  days'  « 


198 


EQUATION    OF  ACCOUNTS. 


25.  Average  the  following  sales  : 
Sept.    4,  1881,  $187.16  on     6  months' credit,  or  30  days  less 


u 

16, 

a 

332.40 

« 

30 

days' 

u 

(( 

24, 

(f 

512.75 

it 

6 

months' 

(I 

or 

30 

days 

less 

Oct. 

5, 

(( 

164.60 

a 

6 

tt 

u 

M 

30 

« 

(t 

t( 

27, 

(f 

187.30 

« 

6 

a 

(( 

tt 

30 

t( 

(t 

Nov. 

5, 

(( 

436.75 

(f 

60 

days' 

(( 

a 

16, 

<( 

126. 

« 

6 

months' 

it 

or 

30 

days 

less 

26.  Average  the  following  account : 

Dec.    1,  1882,  $246.75  on  30  days'  credit. 

"     12,     "  312.40    "  60     "  " 

"     26,     "  819.46    "  4  months'  "      less  5%  30  days. 

Jan.    2,  1883,  674.32    "  4       "  "         "  5$  30  days. 

"     10,     "  126.60    "  60  days' 

Feb.    4,     "  434.50    "     4  months'  "      less  5^  30  days. 


439.  To  find  the  equated  time  for  the  payment  of  the 
balance  of  an  account  having  both  debit  and  credit  items. 

440.  Ex.     At  what  date  may  the  balance  of  the  following 
account  be  paid  without  loss  of  interest  to  either  party? 

Dr.     JOHI*  EOACH  in  account  with  GEO.  H.  STUAKT.       Or. 


1882. 

June    6 

Mdse.  30  da. 

456 

00 

1882. 

July  26 

Cash. 

400 

00 

"    20 

"        60  da. 

384 

00 

Aug.  10 

u 

375 

00 

July     5 

"          3  mo. 

216 

00 

"    10 

Mdse.  60  da. 

288 

00 

"    26 

"          3  mo. 

552 

00 

441.  OPERATION. 

Due  Dr. 

July     6,   $456  x      0  =          0 
Aug.  19,     384  x    < 
Oct.      5,     216  x     ! 
"      26,  _552  x  1: 
1608 
1063 
545 


PRODUCT  METHOD. 

Due 


Cr. 


July  26,    $400  x  20  = 
X  35   = 

X  95   = 


16896 
19656 
61824 

Aug. 
Oct. 

10, 
9, 

375 

288 

1063 

98376 

48485 

8000 
13125 
27360 

48485 


)  49891  (  92  days  after  July  6,  or  Oct.  6. 


EQUATION    OF   ACCOUNTS.  199 

ANALYSIS. — First  find  the  due  date  of  each  item.  For  convenience, 
assume  July  6,  the  earliest  due  date,  as  the  day  of  settlement  for  all  the 
items  on  each  side  of  the  account.  (See  Art.  433,  Note  2.)  If  the  balance 
of  the  account  is  paid  July  6,  the  assumed  date  of  settlement,  there  would  be 
a  loss  to  the  payer,  on  the  debit  side  of  the  account,  equivalent  to  the  interest 
of  $98376  for  1  day,  and  on  the  credit  side,  of  $48485  for  1  day  ;  or  a  net  loss 
of  $49891  for  1  day,  or  of  $545  for  92  days.  Since  the  loss  of  interest  to  the 
payer  by  settling  the  account  July  6,  is  equivalent  to  the  interest  of  the 
balance,  or  the  amount  paid,  for  92  days,  it  is  evident  that  the  day  when  there 
would  be  no  loss  of  interest  must  be  92  days  after  July  6, 1882,  or  Oct.  6,  1882. 

If  the  greater  sum  of  the  products  had  been  on  the  credit  side,  there 
would  have  been  a  gain  to  the  payer  by  settling  the  account  July  6,  and  the 
day  that  the  balance  of  the  account  would  commence  to  draw  interest  would 
have  been  92  days  bsfore  July  6,  or  Apr.  5,  1882. 

442.  EULE  FOR  THE  PEODUCT  METHOD. — First  find  the 
due  date  of  each  item.  Assume  the  earliest  due  date  as  the 
day  of  settlement  for  cull  the  items  on  both  sides  of  the  ac- 
count. Multiply  each  item  by  the  number  of  days  inter- 
vening between  the  assumed  date  of  settlement  and  the  due 
date  of  the  item,  and  find  the  sum  of  the  products  on  each 
side  of  the  account.  Divide  the  balance  (the  difference  be- 
tween the  sums  of  the  debit  and  credit  products)  of  the 
products  by  the  balance  of  the  account.  The  quotient  will 
be  the  number  of  days  intervening  between  the  assumed 
date  and  the  true  date  of  settlement. 

To  find  the  true  date  of  settlement,  count  forward  from 
the  assumed  date,  when  the  balance  of  the  account  and  the 
balance  of  the  products  are  on  the  same  side  (both  debits  or 
both  credits) ;  and  count  backward,  when  on  opposite  sides. 

NOTE.— 1.  The  rule  for  counting  backward  and  forward  is  the  reverse  of 
the  above,  when  the  latest  date  or  a  date  after  the  latest  date  is  taken  as  the 
assumed  date  of  settlement. 

2.  Although  the  principles  of  equation  of  accounts  are  theoretically  correct, 
they  are  not  always  practicable  and  can  not  be  legally  enforced.     Thus,  if  a 
debt  of  $4000  is  due  Feb.  1,  no  merchant  would  accept  a  payment  of  $3600, 
Jan.  1,  with  the  understanding    that  the   remaining   $400  would  remain 
unsettled  9  months  after  Feb.  1,    or  until  Nov.  1.     The  merchant   would 
undoubtedly  be  willing  to  allow  a  discount  equivalent  to  the  interest  of  $3600 
for  the  unexpired  time,  or  1  month. 

3.  In  finding  the  equated  time,  reject  the  cents  when  less  than  50 ;  and 
add  1  dollar  to  the  dollars  when  the  cents  are  more  than  50.     The  results  will 
be  sufficiently  accurate. 


200 


EQUATION    OF   ACCOUNTS. 


443.  OPERATION. — FIRST  INTEREST  METHOD.* 


Dr. 


Due 

July     6, 
Aug.  19, 
Oct.      5, 
"      26, 

$456 
384 
216 
552 

Days. 
0 

44 
91 
112 

Interest. 

$0.00 
2.816 
3.276 
10.304 

1608 
1063 

16.396 

8.08 

Or. 

Due  Days.  Inteiest. 

July   26,     $400  20  $1.333 

Aug.  10,       375  35  2.187 

Oct.      9,     _288  95  4._56_ 

1063  8.080 


60  )j>.45__          )  8.3160  (  92  days  after  July  6,  or 

.0908  Oct.  6,  1882. 

ANALYSIS. — If  the  account  is  settled  July  6,  the  assumed  date  of  settle- 
ment, Mr.  R.  would  be  entitled  to  a  discount  on  the  debit  side  of  $16.396,  and 
Mr.  S.  on  the  credit  side  of  $8.08;  or,  Mr.  R.  would  be  entitled  to  a  net  dis- 
count of  $8.316.  If,  by  paying  the  balance  of  the  account,  July  6,  Mr.  R.  is 
entitled  to  a  discount  of  $8.316,  it  is  evident  that  he  should  be  allowed  to 
defer  payment  until  the  balance  would  produce  an  equivalent  interest,  or  92 
days.  Hence,  the  true  date  of  settlement  is  92  days  after  July  6,  1882,  or 
Oct.  6, 1882. 

When  the  balance  of  the  account  and  the  balance  of  interest  are  both  due 
the  same  party,  the  equated  time  is  previous  to  the  assumed  date  of  settle- 
ment ;  and,  when  the  balance  of  the  account  and  the  balance  of  interest  are 
due  different  parties,  the  equated  time  is  after  the  assumed  date. 

444.  In  the  following  operation,  the  latest  due  date  is  assumed 
as  the  date  of  settlement  for  all  the  items  : 


Due 

July  6, 

Aug.  19, 

Oct.  5, 

"  26, 


60)5.45     .0908)1.8590  (  20  days  before  Oct.  26,  or 

.0908  Oct.  6,  1882. 

ANALYSIS. — If  the  account  is  settled  Oct.  26,  the  assumed  date  of  settle- 
ment, the  payer  will  be  obliged  to  pay  $1.859  interest  in  addition  to  the 
balance  of  the  account.  Hence,  the  date  when  the  balance  only  may  be  paid 
without  loss  to  either  party  must  be  20  days  before  Oct.  26, 1882,  or  Oct.  6, 1882. 


Days. 

OPERATION. 

Interest.                    Due 

Days. 

Interest 

$456 

112 

$8. 

512 

July 

26, 

$400 

92 

$6. 

133 

384 

68 

4. 

352 

Aug. 

10, 

375 

77 

4. 

812 

216 

21 

. 

756 

Oct. 

9, 

288 

17 

. 

816 

552 

0 

. 

00 

1063 

11. 

761 

1608 

13. 

620 

1063 

11. 

761 

*  See  Art.  436. 


EQUATION    OF  ACCOUNTS, 


445.  OPERATION. — APPROXIMATE  INTEREST  METHOD.* 


201 


Dr. 

Cr. 

Mo.          Days. 

Credit. 

Interest. 

Mo.         Days. 

Credit. 

Interest. 

0 

June    6, 

1456  30 

da.    j 

$2.28 
.456 

1  July  26, 

$400 

$2.00 
1.333 

/• 

3.84 

40 

0 

"    20, 

38460 

da.    -j 

1  28 

\ 

•  TtV/ 

3  75 

1 

July     5, 

216    3 

mo.    \ 

( 

-L  •  /WO 

4.32 
.18 
11.04 

2  Aug.  10, 
2     "     10, 

375             j 

288  60  da.  j 

t/«   4  fJ 

.625 
5.76 
.48 

1 

"      26, 

552    3 

mo.  < 

1.84 

1063 

14.348 

( 

.552 

1608 

25.788 

1063 

14.348 

o  \ 

5.45 

2.725) 

11.440  (4  mo.  6  da. 

after  May  31 

,  or 

2.725 

10.900 

Oct.  6. 

.540 

30 
2.725)16.200(6  days. 

EXAM  PLES. 

446.     1.  At  what  date  may  the  balance  of  the  following 
account  be  paid  without  loss  to  either  party  ? 


Dr. 


ISAIAH  B.  PRICE. 


Or. 


1832. 

1883. 

May  16 

To  Mdse. 

437 

00 

May  23 

By  Cash. 

400 

00 

"     31 

«       « 

324 

00 

I  June  16 

«         « 

300 

00 

2.  Find  the  average  date  of  maturity  for  the  balance  of  the 
following  account : 

Dr.  WILLIAM  C.  DOUGLAS.  Cr. 


1881. 

1881. 

Jan.     4 

Mdse.  30  da. 

516 

00 

Feb.    1 

Cash.     .     . 

500 

00 

"     28 

"      60  da. 

325 

00 

"       1 

Note  60  da. 

300 

00 

Feb.     4 

"        4  mo. 

437 

00 

*  Ses  second  interest  method,  Art.  437,  and  second  method,  Ex.  14,  page  194. 


202 


EQUATION    OF  ACCOUNTS. 


3.  Average  the  following  account : 
Dr.  JOSEPH  H.  WEIGHT. 


Or 


1882. 

1882. 

Mar.  27 

Mdse,    4  mo. 

716 

48 

Apr.  16 

Cash.    .     . 

300 

Apr.  16 

"       60  da. 

325 

75 

May    2 

u 

400 

May     1 

"         4  mo. 

413 

40 

July    8 

u 

500 

June    4 

"         4  mo. 

716 

87 

4-  What  is  the  equated  time  for  the  payment  of  the  balance  of 
the  following  account  ? 

Dr.  A  in  account  with  B.  Or. 


1882. 

Mar.  16 

Mdse.    4  mo. 

444 

57 

1882. 

July     1 

Cash.      .    . 

400 

"      30 

"     60  da. 

376 

82 

"      20 

a 

375 

Apr.  20 

"     30  da. 

712 

19 

Aug.  16 

tt 

700 

May  17 

4  mo. 

628 

75 

"    30 

a 

600 

"     28 

4  mo. 

419 

31 

5.  Average  the  following  account.     What  will  be  the  amount 
due  Jan.  1,  1882  ? 
Dr.  C  in  account  with  D.  Or. 


1881. 

1881. 

June  16 

Mdse.  30  da. 

517 

25 

June  16 

Note  60  (63)  da. 

1000 

"     28 

"     60  da. 

487 

50 

July  30 

Cash.       .     . 

375 

July    5 

"       4  mo. 

816 

75 

Aug.  13 

Mdse.  4  mo. 

900 

"     21 

"       6  mo. 

924 

30 

Oct.     5 

Cash.       .     . 

500 

Aug.  12 

"       4  mo. 

317 

65 

• 

6.  When  will  the  balance  of  the  following  account  commence 
drawing  interest  ?     How  much  would  be  due  Mar.  1,  1883. 

Dr.  ANDREW  CARNEGIE,  Pittsburg,  Pa.  Or. 


1882. 

Sept.     4 

Cash 

100 

1882. 

Aug.  16 

Mdse.     4  mo. 

647 

13 

4 

Note  4  mo. 

900 

"      29 

"         4  mo. 

322 

85 

Oct.     31 

Cash 

250 

Sept.     4 

"         4  mo. 

412 

90 

Dec.    28 

it 

600 

"      17 

"         4  mo. 

588 

33 

"      17 

30  da. 

246 

12 

Nov.     4 

"         4  mo. 

683 

45 

EQUATION    OF   ACCOUNTS    SALES. 


203 


7.  Find  the  equated  time  for  the  payment  of  the  balance  of  the 
following  account. 

Dr.  JAMES  B.  FARWELL,  Chicago,  111.  Cr. 


1881. 

1881. 

Jan.      4 

Mdse.    4  mo. 

637 

20 

Mar.   16 

Cash. 

300 

00 

"       14 

4  mo. 

412 

87 

Apr.    20 

u 

400 

00 

"       14 

60  da. 

214 

35 

May      3 

n 

200 

00 

Mar.    16 

"         4  mo. 

298 

60 

3 

Note  4  mo. 

800 

00 

"       28 

"       30  da. 

973 

25 

8.  Average  the  following  account : 
Dr.  ARNOLD,  CONSTABLE,  &  Co. 


Or. 


1882. 

Apr.      4 

Mdse.     4  mo. 

426 

32 

1882. 

Apr.    25 

Cash. 

375 

"       20 

Cash. 

387 

40 

June  30 

(4 

600 

May    13 

60  da. 

622 

39 

July    31 

Note  60  da. 

600 

"       27 

"       30  da. 

584 

75 

Aug.   15 

Cash. 

500 

July      5 

"         4  mo. 

224 

50 

Oct.    31 

it 

400 

"       16 

11         4  mo. 

838 

95 

447.  To  find  the  equated  time  for  the  payment  of  the 
net  proceeds  (282)  of  an  account  sales  (283). 

448.  1.  The  sales  form  the  credit  side  of  the  account,  and 
fhe  charges  and  advances  the  debit  side. 

2.  The  charges  for  transportation,  cartage,  and  other  items 
paid  by  the  commission  merchant  are  considered  due  at  the  time 
of  the  payment  of  the  same. 

3.  The  commission  and  other  after-charges  of  the  commission 
merchant  are  considered  due  by  some  at  the  average  due  date  of 
the  sales;  and  by  others,  at  the  average  date  of  the  sales.     Since 
the  commission  is  so  small  compared  with  the  gross  sales,  in  many 
examples,  it  makes  no  difference  which  date  the  commission  is 
considered  due.     Certain  merchants  enter  the  commission  at  the 
date  the  account  sales  is  rendered,  and,  by  so  doing,  produce  a 
result  sufficiently  accurate. 

4.  Many  commission  merchants,  when  the  consignments  are  not 
separated  and  numbered,  enter  the  sales  and  commission  only  on 
the  account  sales  (See  Ex.  4,  Art,  45O),  and  enter  the  advances 


204 


EQUATION    OF  ACCOUNTS. 


and  the  general  charges  in  the  account  current  (See  Ex.  6,  Art. 
458).  Accounts  ^Vs,  when  the  shipments  are  continuous,  are 
rendered  montnl^tu  uhe  manufacturers  or  consignors,  and 
"sketches  "  weekjty'ur  whenever  a  sale  is  made. 

5.  With  the  exception  of  finding  the  date  for  the  commission 
and  other  after-charges,  the  process  of  averaging  an  account  sales 
is  exactly  the  same  as  that  of  averaging  an  account 
both  debit  and  credit  items. 

449.     Ex.     What  is  the  equated  time  for  the  payment  of  the 
net  proceeds  of  the  following  account  sales  ? 

NEW  YORK,  Dec.  1,  1881. 
Account  sales  of  Seed 

For  account  of  WILLIAM  STEPHENS  &  Co. 
By  FRANKLIN  EDSON  &  Co. 


1881. 

Nov. 

4 

45^-  bu.  Timothy  Seed    .     30  da. 

IHJL 

79 

53 

a 

18 

50       "    Mammoth  Cl.  Seed  60  da. 

9ILO. 

450 

t( 

28 

49AA   «    Clover  Seed    .     .     Cash. 

gl-fi. 

418 

32 

947 

85 

CHARGES. 

Oct. 

31 

Transportation  

60 

00 

Dec. 

1 

Commission  5%  as  Dec.  22,  1881. 

( 

_47 

39 

107 

39 

Net  proceeds  due  Dec.  26,  1881.    . 

. 

840 

47j 

ANALYSIS.— The  average  due  date  of  the  sales  is  Dec.  22,  1881,  which  is 
taken  as  the  due  date  for  the  commission. 

The  account  sales  to  be  averaged  will  now  be  as  follows  : 


Dr. 

Due   Oct.    31,   1881, 
"     Dec.   22,      " 


Or. 

$60.00  Due  Dec.     4,    1881,  $79.53 

47.39  "     Jan.    17,    1882,  450.00 

"     Nov.  28,   1881,  418.32 

By  averaging  the  above,  we  find  the  net  proceeds,  $840.46,  are  due  Dec. 
26,  1881. 

If  the  commission  is  considered  due  Nov.  21,  1881,  the  average  date  of 
the  sales,  the  net  proceeds  will  be  due  Dec.  28,  1881. 

NOTE. — If  the  same  assumed  date,  or  focal  date,  be  taken  in  finding  the 
average  due  date  of  the  sales  as  in  finding  the  average  due  date  of  the  net 
proceeds,  the  operation  of  the  former  will  form  the  credit  side  of  the  latter 
operation. 


EQUATION    OF   ACCOUNTS    SALES. 


205 


EXAMPLES. 

45O.  Find  the  net  proceeds  and  equated  time  of  the  ioilowing 
accounts  sales.  (Unless  otherwise  stated,  the  commission  is  con- 
sidered due  at  the  average  due  date  of  the  sales.) 

1.  Sales  of  400  bbls.  flour  received  per  N.  Y.  C.  &  H.  R.  R.  R., 
for  account  of  A.  W.  ARCHIBALD,  Ottumwa,  Iowa. 


1881. 

rwi 

j_ 

May 

11 

125bbls.  "  Kirkwood  "  cash,  .     . 

615- 

#** 

a  7f 

^* 

tt 

12 

150     "      "Iowa"          4  mo.,      . 

gin 

tt* 

" 

18 

125     "     "Kirkwood  "4  mo.,      . 

7JUL 

816' 
#*# 

V**i 

tf 

CHARGES. 

May 

3 

Transportation  and  Cartage,      .     . 

. 

425 

tt 

4 

Inspection,  iL     . 

15 

tt 

18 

Storage,  

45 

. 

Commission  and  Guaranty  5%,  .    . 

3S1 

II 

**'* 

*# 

E.  &  0.  E.  E.  R.  LlYERMORE. 

NEW  YORK,  May  20,  1881. 

What  would  be  the  equated  time  for  the  payment  of  the 
above  proceeds,  if  the  commission  and  guaranty  were  considered 
due  at  the  average  due  date  of  the  sales  ?  At  the  average  date  of 
the  sales  ?  If  considered  due  May  18,  the  date  of  the  last  sale  ? 

2.  Account  sales  of  900  sides  hemlock  sole  leather  by  MAS- 
SET  &  JAIS^EY,  for  account  of  GRANT  &  HORTON,  Ridgway, 


1881. 

Aug. 

ft 

Aug. 
tt 

E 
Pi 

14 

18 
21 

2 

& 
aiL. 

Sides. 

Description. 

Terms. 

Weight. 

Price. 

##** 

'Mi 

##** 

it 

it 

** 

#*#* 
*** 

** 
** 

400 

300 
200 

Tran 
Inspe 
Comi 
Proct 
0.  E. 

iDELI 

"Ridgway"  #7 

#7 
88 

CHA 

sportation  $70, 
ction, 

4  mo. 
4  mo. 
30  da. 

RGES. 

Cartag 

9407 
6875 
4712 

e$9,  . 

27 
27J 

#* 

9 
#*# 

r  &  J 

nission  and  Guaranty  5$,      .    . 
;eds  due  ,  1881,     .... 

MASSE3 

»HIA,  PA.,  Aug.  22,  1881. 

##** 

AtfNEY. 

ftt 


206 


EQUATION    OF  ACCOUNTS 


3.  Find  the  equated  time  for  the  payment  of  the  net  proceeds 
of  Ex.  27,  Art.  286,  supposing  that  the  merchandise  was  sold  for 
cash,  and  that  the  commission  was  due  at  the  date  given. 

4.  Sales  by  JAMES  TALCOTT,  New  York,  for  account  of  Phenix 
Mills,  Cohoes,  N.  Y.     March  31, 


Date. 

Cases. 

No. 

Description. 

Time. 

Yards. 

Price. 

Amount. 

Mar.    1 

2 

7619 

Fancy  Cassimere. 

30^0. 

966s 

1.35 

****** 

"     10 

4 

3475 

<(            (( 

10  da. 

1994 

1.70 

****** 

"     13 

3 

4157 

<(            (t 

30  da. 

15061 

2.30 

****  ** 

"    17 

4 

6283 

«                 <e 

4  mo. 

19363 

1.65 

****** 

"    '26 

2 

3971 

(t                 (( 

Cash. 

978 

1.85 

****>** 

Less  Commission  5%, 
Proceeds  due ,  1882, 


*****  ** 
***  ** 


*****  ** 


6.  Account    Sales    of   merchandise  by  JOHN  F.  COOK,   for 
account  of  Excelsior  Packing  Co.,  Cincinnati,  Ohio. 


1881. 

Oct. 

1C 

50  Bbls.  Mess  Beef,      .     .     Cash. 

HJJL 

*** 

** 

(t 

24 

100     "     N.  M.  Pork,     .     . 

17JLJL 

**** 

(f 

31 

25     "     Hams  6376  Ibs.,  .     10  da. 

13^ 

*** 

** 

Nov. 

9 

25     "     Shoulders  5717  Ibs.,  60  da. 

9^ 

*** 

** 

" 

18 

75     "     C.  M.  Pork,     .     .       4  mo. 

13^ 

**** 

** 

**** 

** 

CHARGES. 

Oct. 

13 

Transportation,    

325 

k< 

15 

Cartage, 

37 

50 

« 

15 

Cooperage, 

15 

(( 

15 

Inspection,      

13 

75 

Nov 

18 

Storage, 

48 

75 

Commission  5$,  

*** 

** 

*** 

** 

~N~ot  irpopppfl  s  fJno                Iftftl 

. 

— 

**** 

** 

E.  &  0.  E.                                                  JOHN-  F.  COOK. 

NEW  YORK,  N.  Y.,  Nov.  20,  1881. 

*  If  the  commission  is  considered  due  at  the  average  due  date  of  the  sales,  and  since 
there  are  no  other  changes,  the  net  proceeds  will  be  due  at  the  same  date. 


ACCOUNTS     CURRENT. 


DEFINITIONS. 

451.  An  Account  Current  is  an  itemized  account  of  the 
business  transactions  between  two  houses,  showing  the  balance  or 
amount  due  at  the  current  date.  The  amount  due  is  sometimes 
called  the  cash  balance. 

1.  An  account  current  is  a  transcript  of  the  ledger  account 
with  the  addition  of   certain  details   taken  from  the   books  of 
original  entry,  and  is  arranged  in  a  different  form. 

2.  Interest  is  charged,  or  not,  according  to  the  custom  of  the 
business,  or  the  agreement  between  the  parties.      This  chapter 
treats  only  of  accounts  in  which  interest  is  charged.     When  inter- 
est is  not  charged,  the  balance  due  is  the  difference  between  the 
two  sides  of  the  account  as  originally  entered  in  the  ledger.     The 
interest  may  be  reckoned  according  to  any  of  the  methods  of  Art. 
299.      In  the  illustrative  example   the  exact  time  in  days  is 
found,  and  the  days  are  regarded  as  360ths  of  a  year.     In  the 
examples   for  practice,  unless  otherwise   stated,   the   interest  is 
reckoned  on  the  same  basis. 

3.  Accounts  current  are  rendered  by  merchants,  bankers,  and 
brokers    annually    (Ex.    2),    semi-annually    (Ex.    1),     quarterly 
(Ex.3),  or  monthly  (Ex.  6).      Since  the  interest  draws  interest 
after  the  account  is  balanced,  the  oftener  the  account  is  balanced, 
or  the  interest  is  added  to  the  account,  the  greater  the  amount 
due.     Some  merchants  render  partial  accounts  current  monthly, 
but  do  not  carry  the  interest  to  the  main  column  until  the  end  of 
the  year  (Ex.  11).    The  twelve  partial  accounts  current  make,  when 
combined,  the  complete  account  current  for  the  whole  year. 

4>  There  are  three  methods  in  common  use  for  finding  the 
amount  due  on  an  account,  including  interest,  at  a  certain  date, 
all  of  which  are  presented  in  the  following  illustrative  example  : 
1.  By  interest ;  2.  By  products  ;  3.  By  daily  balances. 


208 


ACCOUNTS    CURRENT. 


4:52.  Ex.     Find  the  amount  due,  including  interest  at  6$,  on 
the  following  account  Jan.  1,  1882. 


Dr.        GEO.  W.  CHILDS  in  account  with  A.  A.  Low. 


Or. 


1881. 

1881. 

Oct.     1 

Balance. 

1800 

Oct.  31 

Cash. 

1000 

"    16 

Mdse.  30  da. 

360 

Nov.  16 

NoteSOtfa. 

600 

Nov.  27 

30  da. 

432 

Dec.    4 

Cash. 

240 

Dec.  18 

BillofH.O.&Co. 

420 

"     26 

u 

300 

453.  OPERATION. — INTEBEST  METHOD. 


Dr. 

Cr. 

Due. 

Amount. 

Days. 

Interest. 

Due. 

Amount. 

Days. 

Interest. 

Oct. 

1, 

$1800 

92 

$27. 

60 

Oct. 

31, 

$1000 

62 

$10. 

33 

Nov. 

15, 

360 

47 

2. 

82 

Dec. 

19, 

600 

13 

1. 

30 

Dec. 

27, 

432 

5 

. 

36 

it 

4, 

240 

28 

1. 

12 

K 

18, 

420 

14 

. 

98 

tt 

26, 

300 

6 

, 

30 

$3012 

$31. 

76 

$2140 

$13.05 

2140 

13. 

05 

872 


18.71  =  890.71. 


ANALYSIS. — First  find  the  due  date  of  each  item  of  the  account.  Each 
item  will  draw  interest  from  its  due  date  until  the  day  of  settlement,  or  Jan. 
1,  1882.  The  total  interest  on  the  debit  side  of  the  account  is  $31.76,  and  on 
the  credit  side,  $13.05.  The  balance  of  interest,  $18.71,  is  therefore  in  favor 
of  the  debit  side,  or  is  due  Mr.  Low. 

Since  both  the  balance  of  the  account  ($872)  and  the  balance  of  interest 
($18.71)  are  due  the  same  party,  the  net  amount  due  Jan.  1,  1882,  is  f  872  plus 
$18.71,  or  $890.71. 

If  the  balance  of  interest  had  been  on  the  credit  side  of  the  account,  the 
net  amount  due  would  have  been  $872  minus  $18.71,  or  $853.29. 

NOTES. — 1.  It  will  sometimes  happen  that  certain  items  will  fall  due 
after  the  day  of  settlement.  The  interest  on  such  items  should  be  transferred 
to  the  opposite  side  of  the  account.  (See  Ex.  8.) 

2.  If  the  account  has  been  averaged,  the  amount  due  at  a  given  date  may 
be  found  by  calculating  the  interest  on  the  balance  of  the  account  from  the 
time  it  is  due  to  the  date  of  settlement.     If  the  date  of  settlement  is  earlier 
than  the  average  date,  subtract  the  interest  from  the  balance  of  the  account ; 
if  later  than  the  average  date,  add  the  interest.     (See  Art.  438,  Ex.  7,  Note.) 

3.  The  interest  method  is  generally  used  in  business.     Since  it  gives  the 
interest  on  each  item  and  is  readily  understood,  it  is  more  satisfactory  to  those 
to  whom  accounts  current  are  sent  than  the  product  method.     When  interest 
tables  are  used,  it  is  shorter  than  any  other  method. 


ACCOUNTS    CURRENT. 


209 


454.  The  following  is  a  common  form  of  an  account  current 
including  interest : 

Dr.       GEO.  W.  CHILDS  in  %  current  with  A.  A.  Low.       Or. 


1881. 

Days. 

Interest. 

Amounts. 

1881. 

Days. 

Interest. 

Amounts. 

Oct.     1 

Balance. 

92 

27.60 

1800.00 

Oct.  31 

Cash. 

62 

10.33 

1000.00 

"      16 

Mdse.  as  Nov.  15. 

47 

2.82 

360.00 

Nov.  16 

Note  as  Dec.  19. 

13 

1.30 

600.00 

Nov.  27 

"  Dec.  27. 

5 

.36 

432.00 

Dec.    4 

Cash. 

28 

1.12 

240.00 

Dec.  18 

BillofH.C.  &Co. 

14 

.98 

420.00 

"     26 

" 

6 

.30 

300.00 

1882. 

1882. 

Jan.    1 

Bal.  of  Interest. 

18.71 

Jan.    1 

Bal.  of  Interest. 

18.71 

"       1 

"     "  Account. 

890.71 

1882. 

31.76 

3030.71 

31.76 

3030.71 

Jan.    1 

Balance. 

890.71 

455.  EULE  FOR  THE  INTEREST  METHOD. — First  find  the 
due  date  of  each  item  of  the  account.     TJien  find  the  inter- 
est on  each  item  from  the  date  it  becomes  due  to  the  day  of 
settlement.      The  difference  between  the  sums  of  the   debit 
and  the  credit  interest  will  be  the  balance  of  interest. 

To  find  the  net  amount  due,  ivhen  the  balance  of  interest 
and  the  balance  of  items  are  on  the  same  side,  take  their 
sum ;  ^vhe^^  on  opposite  sides,  talce  their  difference. 

456.  OPERATION:. — PRODUCT  METHOD. 


Dr. 

Or. 

Due. 

Am't. 

Days. 

Products. 

Due. 

Am't. 

Days 

Products. 

Oct. 

1, 

$1800 

X 

92  = 

165600 

Oct. 

31, 

$1000 

X 

62 

=  62000 

Nov. 

15, 

360 

X 

47  = 

16920 

Dec. 

19, 

600 

X 

13 

=  7800 

Dec. 

27, 

432 

X 

5  = 

2160 

a 

4, 

240 

X 

28 

=  6720 

a 

18, 

420 

X 

14  = 

5880 

a 

26, 

300 

X 

6 

=  1800 

$3012 

190560 

$2140 

78320 

2140 

78320    $872 

+  $18.71  =  $890.71. 

872 


6 )  112240 


$18.706 

ANALYSIS. — By  multiplying  the  number  of  dollars  by  the  number  of  days, 
and  taking  the  sum  of  the  products  on  each  side  of  the  account,  we  find  that 
the  total  debit  interest  is  equivalent  to  the  interest  of  $190560  for  1  day,  and 
the  total  credit  interest  to  the  interest  of  $78320  for  1  day.  The  balance  of 
interest  is  therefore  equivalent  to  the  interest  of  $112340  for  1  day.  The 
interest  of  $1  for  1  day  is  $  of  a  mill  (311,  3),  and  of  $112240, 18706  (£  of  112240) 
mills,  or  $18.71.  Since  the  balance  of  items  ($872)  and  the  balance  of  interest 
($18.71)  are  both  due  the  same  party,  the  net  amount  due  is  their  sum,  or  $890.71. 


210  ACCOUNTS  CURRENT. 

457.  OPERATION. — BY  DAILY  BALANCES. 


Date. 

Dr. 

Cr. 

Dr.  Balances. 

Days. 

Dr.  Products. 

Oct.  1 

1800 

1800 

30 

54000 

"  31 

1000 

800 

15 

12000 

Nov.  15 

360 

1160 

19 

22J040 

Dec.  4 

240 

920 

14 

12880 

"  18 

420 

1340 

1 

1340 

"  19 

600 

740 

7 

5180 

"  26 

300 

440 

1 

440 

«  27 

432 

872 

5 

4360 

3012 

2140 

92 

6  )  112240 

2140 
872  +  18.71  =  890.71. 


18.706 


ANALYSIS.— Arrange  the  debit  and  the  credit  items  in  the  order  of  their 
dates  as  in  the  operation.  Find  the  balance  of  the  items  at  each  of  the  dates. 
There  is  a  debit  balance  of  $1800  for  30  days  ;  the  interest  of  which  is  equiv- 
alent to  the  interest  of  $54000  for  1  day.  The  interest  of  the  next  balance, 
$800,  for  15  days  is  equivalent  to  the  interest  of  $12000  for  1  day,  etc.  The 
total  balance  of  interest  is  equivalent  to  the  interest  of  $112240  for  1  day,  or 
$18.71.  The  net  amount  due  is  $872  plus  $18.71,  or  $890.71.  (See  Art.  311, 
Note  3.) 

NOTE. — If,  at  any  time  in  the  above  operation,  there  had  been  a  credit 
balance,  it  would  have  been  necessary  to  have  had  additional  columns  for 
"Cr.  Balances5'  and  "Or.  Products." 


EXAM  PLES. 


458.     1.  Find  the  balance  due  on  the  following  account,  Jan. 
1,  1883,  interest  being  reckoned  at  6%. 


Dr. 


HOWAKD  THORNTON. 


Cr. 


1882. 

July    1 

Aug.  24 
Oct.  18 

Balance. 
Mdse. 
Draft  C.&C. 

1830 
448 

387 

45 

00 
40 

1882. 

Sept.  13 
Oct.  31 

Nov.    5 

Net  Proceeds. 
a          (( 

Cash. 

876 
912 
1000 

40 
36 
00 

Dec.  12 

Draft  H.  &  Co. 

516 

88 

ACCOUNTS    CURRENT. 


211 


2.  What  is  the  net  amount  due  on  the  following  account, 
July  1,  1882,  at  §%  ? 

Dr.   C.  H.  MILLS  in  %  current  with  G.  F.  SWOETFIGUER.   Cr. 


1881. 

1881. 

July     1 

Balance. 

1275 

46 

Nov.  14 

Mdse.    4  mo. 

587 

19 

Sept.  13 

Draft  #1012. 

871 

52 

1882. 

1882. 

Mar.  13 

"      30  da. 

612 

35 

Jan.      4 

"      #1017. 

913 

27 

Apr.  27 

"       60  da. 

846 

93 

May    17 

"      #1024. 

345 

63 

June    3 

Cash. 

500 

00 

8.  What  is  the  balance  of  the  following  account,  Apr.  1,  1882, 


at 


Dr.    W.  J.  HILLIS  in  account  with  LANGRAVE  SHULTS.     Cr. 


1882. 

1882. 

Jan.  16 

Dft.  M.  &  C. 

937 

64 

Jan.     1 

Balance. 

3456 

75 

"      31 

"    B.  &  D. 

856 

75 

u      27 

Sales  as  Mar.  15 

1225 

19 

Mar.    3 

«     W.  &  Y. 

1749 

30 

Feb.    4 

Mdse  as  Mar.    6 

673 

75 

"     24 

«    V.  &0. 

912 

38 

"     28 

Sales  as  Mar.  19 

2428 

35 

4.  Find  the  amount  due  Aug.  1,  at  6%,  on  the  account  repre- 
sented in  Ex.  7,  Art.  438.     (See  Note,  Ex.  7,  Art.  438.) 

5.  Find  the  amount  due  Oct.  1,  1882,  at  6%,  on  the  account 
represented  in  Ex.  4,  Art.  446. 

6.  Find  the  balance  due  Apr.  1,  1882,  at  6$,  on  the  following 
account  current. 

PHENIX  MILLS  in  %  current  with  JAMES  TALCOTT,  New  York, 
Apr.  1,  1882. 


Date. 

Dr. 

Amounts. 

Date. 

Cr. 

Amounts. 

1882. 

1882. 

Mar.    1 

Balance. 

45108 

34 

Mar.  31 

Net  Proceeds 

«     16 

Draft  #676. 

1000 

of  Account 

"     18 

"     #675. 

2000 

Sales  due  Apr. 

"     24 

"     #678. 

5000 

26,  1882. 

12505 

70 

"    28 

Cotton  Bill. 

3176 

42 

(See  Ex.  4, 

"    30 

Transportation. 

875 

10 

Art.  45O.) 

212 


ACCOUNTS    CURRENT. 


7.  Find  the  gain  or  loss  on  the  following  consignment  account, 
taking  as  the  day  of  settlement  Jan.  29,  1881,  the  day  the  draft 
for  the  balance  of  the  account  was  drawn  and  sold,  and  reckoning 
interest  at  6%  (365  days  to  the  year). 

Cons.  F.  L.  BRUCKMANN,  #14. 


I860. 

Apr. 
<( 

25 
25 

Dr. 
Mdse.  Net  Cash.                                 ) 
Clearance.                                             3 

Days. 

Interest. 

Amounts. 

279 

300 

17 

(6544 

72 
20 

May 

10 

Insurance. 

*## 

* 

•ir-A- 

40 

1881. 

Jan. 

29 

Balance  of  Interest  to  debit. 

##* 

w* 

« 

1880. 
May 
Nov. 

29 

7 
20 

Gain. 
Or. 

Draft  18000  Reiclismarks 
"       2000 

**# 
** 

### 

*** 

## 

** 

#### 

** 

*** 
* 

•*•:;• 
*•* 

4258 
468 

42 

75 

1881. 
Jan. 

29 

"       9998 

0 

2368 

28 

29 

Balance  of  Interest  to  debit. 

**# 

-::•* 

*## 

** 

**** 

#-x- 

8.  What  was  the  amount  due  on  the  following  account  Feb. 
13,  1881,  the  estimated  due  date  of  a  sight  draft  drawn  Jan.  29, 
1881,  for  the  balance,  reckoning  interest  at  5%  (365  days  to  the 
year)  ? 

F.  L.  BRUCKMANN  on  account  of  Consignment  #14. 


1880. 

Dr. 

Days. 

Interest. 

Amounts. 

Oct. 

25 

Account  Sales                 due  Jan.  9,  1881 

35 

44 

80 

9344 

82 

Dec. 

31 

"    Mar.  7,  1881 

22417 

54 

1881. 

Feb. 

13 

Balance  of  Interest  to  credit. 

*** 

** 

**# 

** 

***** 

** 

1880. 

Cr. 

June 

30 

Freight                             due  May  14,  1880 

*** 

#* 

** 

1176 

32 

May 

6 

Draft  60  days'  sight        "    July  18,  1880  I 

*** 

*** 

** 

j    8000 

»« 

6 

lk     GO     "           "            "       "     18,  1880  ) 

e  10080 

Nov. 

19 

"     60     "          "           "    Feb.    1,1881 

*# 

* 

** 

2000 

1881. 

Feb. 

13 

Interest  Km.  22417.54      "    Mar.    7,  1881 

** 

** 

** 

" 

13 

Balance  of  Interest  to  credit. 

*#* 

** 

Jan. 

29 

Draft  at  sight  to  balance  due  Feb.  13,  1881 

**** 

## 

*** 

** 

***** 

** 

ACCOUNTS    CURRENT. 


213 


NOTES. — 1.  The  interest  on  all  items  falling  due  after  the  day  of  settle- 
ment should  be  entered  in  the  interest  column  on  the  opposite  side  of  the 
account. 

Some  accountants  enter  these  items  of  interest  on  the  same  side  of  the 
account  in  red  ink  so  that  they  will  not  be  added  to  the  other  items,  and  transfer 
the  "  red  interest "  in  one  amount  to  the  opposite  side. 

2.  The  foregoing  represents  an  account  in  German  marks  (reichsmarks)  kept 
in  an  auxiliary  book  by  a  consignor  of  merchandise  to  a  commission  merchant 
at  Hamburg,  Germany. 

The  due  dates  of  drafts,  accounts  sales,  and  other  items  are  obtained 
from  the  letters  from  the  commission  merchant  and  from  accounts  sales  and 
memoranda  rendered  by  him.  The  corresponding  consignment  account  as 
entered  in  the  books  of  the  consignor  is  represented  in  Ex.  7. 

9.  What  was  the  balance  due  Jan.  1,  1882,  at  6$,  on  the 
account  represented  in  Ex.  5,  Art.  446. 

10.  Find  the  amount  due  Mar.  1,  1883,  at  6$,  on  the  account 
represented  in  Ex.  6,  Art.  446. 

11.  Calculate  the  interest  Jan.  1, 1883,  in  the  following  partial 
account  current,  and  find  the  total  amounts.      (Interest  6$,  365 
days  to  the  year. )     (See  Art.  451,  3. ) 


G.  D.  SLOCUM  in  account  with  W.  B. 


1882. 

Dr. 

Days. 

Interest. 

Amounts. 

May 

1 

Totals  from  statement  of  May  1.  1882. 

1387 

63 

28765 

72 

tt 

6 

Draft  H.  B.  Claflin  &  Co. 

240 

50 

71 

1285 

43 

K 

9 

"     Austin,  Nichols  &  Co. 

*•** 

#* 

*•* 

674 

89 

* 

13 

"    W.  H.  Schieffelin  &  Co. 

*** 

** 

#* 

346 

27 

a 

25 

"    Early  &  Lane. 

##* 

** 

*# 

418 

43 

« 

28 

"    Mitchell,  Vance  &  Co. 

#** 

** 

** 

576 

80 

**** 

*# 

***** 

** 

1882. 

Or. 

May 

1 

Totals  from  statement  of  May  1,  1882. 

973 

42 

22413 

71 

«< 

5 

Sales  as  June  28,  1882. 

#•*•» 

#** 

vr-iv 

7316 

84 

ti 

12 

"      "   Aug.     1,  1882. 

*** 

#* 

** 

2110 

92 

" 

18 

"      "  July  13,  1882. 

*** 

*## 

** 

13446 

85 

" 

25 

Cash. 

**# 

#* 

** 

2000 

**** 

** 

***** 

** 

214 


ACCOUNTS    CURRENT. 


12.  Find  the  balance  due  on  the  following  account  Feb.  13, 
1881.     (5$,  365  days  to  the  year.) 

Dr.      A.  WEIN  GREEN  &  Co.,  on  account  of  Cons.  #25.       Cr. 


Date. 

Days. 

Interest 

Amounts. 

Date. 

Days. 

Interest. 

Amoun 

1881 

1880. 

Dec. 

3! 

Ace.  Sales 

Aug. 

5 

Freight. 

*** 

Ml 

** 

653 

due  Feb. 

Nov. 

19 

Draft  due  Feb.  1,1881. 

M 

M 

*# 

18<X)0 

19,  1881. 

22537 

89 

1881. 

Feb. 

13 

Interest  Rm.  22587.89. 

* 

** 

** 

1881. 

Feb. 

13 

Balance  of  Interest. 

M 

Feb. 

13 

Balance  of 

Jan. 

2<; 

Draft  to  balance  due 

Interest. 

** 

w 

** 

~^z 

Feb.  13,  1881. 

**** 

+* 

** 

** 

***** 

13.  Find  the  net  gain  'or  loss  on  the  following  consignment 
account,  Jan.  29,  1881.     (Interest  6$,  365  days  to  the  year.) 


Dr. 


Cons.,  A.  WEINGREEN  &  Co.,  #25. 


Cr. 


Date. 

Days. 

Interest. 

Amounts. 

Date. 

Days. 

Interest 

Amoui 

1880. 

1830. 

June 

3!) 

Mdse. 

##* 

*#* 

** 

49S2 

86 

Nov. 

20 

Draft  Rm.  18000 

** 

** 

** 

4218 

July 

•- 

Clearance. 

*»•* 

** 

20 

1881. 

Aug. 

1 

Insurance. 

*** 

#* 

25 

Jan. 

29 

"        "     38G9 

0 

916 

1881. 

" 

2'' 

Bal.  of  Interest. 

*** 

** 

Jan. 

29 

Bal.  of  Interest. 

*** 

#* 

" 

:9 

Gain. 

** 

** 

**# 

M 

***•» 

«* 

#*# 

** 

**** 

14.  Find  the  amount  due  July  1, 1881,  on  the  account  repre- 
sented in  Ex.  7,  Art.  446. 

15.  What  was  the  balance  due  Jan.  1,  1883,  on  the  account 
represented  in  Ex.  8,  Art.  446  ? 

16.  Find  the  balance  of  the  following  account,  Mar.  31,  1882, 
at  6#. 

Dr.    JAMES  A.  DOUGLAS  in  %  current  with  J.  H.  HOYT.    Cr. 


1882. 

1882. 

Feb.  28 

Balance. 

18452 

50 

Mar.  8 

100  N.  Y.C. 

14537 

50 

Mar.  2 

Draft. 

700 

"  11 

50H.&St.J. 

5162 

50 

"  11 

100  N.  W. 

14062 

50 

"  17 

Cash. 

16000 

«  18 

200H.&St.J. 

20875 

"  24 

100  N.  W. 

14437 

50 

ACCOUNTS    CURRENT. 


215 


17.  What  was  the  balance  due  Feb.  13,  1880,  on  the  following 
account?     (Interest  5$,  365  days  to  the  year.) 

F.  L.  BRUCKMANN"  on  account  of  Consignment  #10. 


Dat 

1879. 
Jan. 
June 
Dec. 
1880. 
Feb. 

1878. 
Oct. 
Nov. 
Dec. 
1879. 
Nov. 
1880. 
Feb. 
Feb. 
Jan. 

L 

accoi 

3. 

23 

30 
31 

13 

22 
30 
10 

19 

13 
13 
29 

?.    ' 

mt 

Dr. 

Account  Sales  due  Mar.    1,  1879. 
"    Aug.    9,  1879. 
"    Feb.  25,  1880. 

Balance  of  Interest  to  credit. 
Cr. 

Freight,                        as  Oct.   22,  1878. 
Telegrams,                    "  Nov.  80,  1878. 
Draft  60  days'  eight  due  Feb.  25,  1879. 

"     60     "       "       "    Feb.    1,  1880. 

Interest  Em.  20334.43  "      "      25,  1880. 
Balance  of  Interest  to  credit  due  Feb.  13,  1880. 
Draft  at  sight  to  balance. 

Find  the  net  gain  or  loss  on  the 
(Interest  6%,  365  days  to  the  ye 
Cons.,  F.  L.  BRUCKMAIO 

Days. 

Interest. 

Amounts. 

*** 
**# 

*** 
*** 
*** 

#* 
** 
0 

follow 
ar.) 

r,  «10. 

**** 
**# 

#** 

** 
** 

** 

21346 
9896 
20334 

02 
13 
43 

*# 

**** 

** 

***** 

#* 

<c 

**** 
** 
** 

** 

** 
** 

*:ft 
** 

1298 
88 
31000 

10000 

*** 

**** 

55 

** 
** 

**** 

** 

***** 

*+ 

ing  consignment 

Date. 

Dr. 
Mdse.     Net  Cash. 
Clearance. 
Insurance. 

Balance  of  Interest  to  debit. 

Cr. 
Draft  31000  Reichsmarks. 

Damage  allowed  by  Insurance  Co. 
Draft  10000  Reichsmarks. 

"       8826 
Balance  of  Interest  to  debit. 
Loss. 

Days. 

Interest. 

Amounts. 

1878. 
Aug. 
« 

Sept. 
1880. 
Jan. 

1878. 
Dec. 
1879. 
Mar. 
Nov. 
1880. 
Jan. 

u 

« 

28 
30 
10 

29 

11 

26 
20 

29 
29 
29 

519 
*** 
**# 

*** 

*** 
** 

0 

**** 
* 

#* 
## 
#* 

13028  ' 

112 

#•** 

48 
20 

** 

**** 

*# 

***** 

** 

*** 

** 
** 

*** 

** 
** 

*•:•? 
** 

7283 

1085 
2343 

2090 
*** 

79 

20 

75 

66 

** 

#**# 

*•::• 

***** 

*# 

STOCKS    AND    BONDS.' 


DEFINITIONS. 

459.  The  term  "  Stock  "  is  applied  to  the  share  capital  of  a 
company,  and  represents  an  interest  in  its  property  over  and  above 
its  liabilities,  and  in  the  profits  of  its  business  after  the  expenses 
and  interest  on  its  bonds  have  been  paid.      This  profit,  when 
divided  among  the  stockholders,  is  known  as  a  dividend.     The 
dividend  is  a  certain  amount  per  share,  or  a  certain  per  cent, 
of  the  ,par  value  of  the  stock. 

1.  The  Capital  Stock  of  a  company  is  divided  into  shares  usually  of  $100 
each.     Shares  of  $50  and  $25  are  called  half-stock  and  quarter-stock  respec- 
tively. 

2.  A  Stock  Certificate  is  a  written  instrument  issued  by  a  company,  and 
signed  by  the  proper  officers,  certifying  that  the  holder  is  the  owner  of  a  cer- 
tain number  of  shares  of  its  Capital  Stock. 

3.  The  sum  for  which  the  shares  or  certificates  were  issued  is  called  the 
Par  Value,  and  the  amount  for  which  they  can  be  sold,  the  Market  Value. 

460.  A  Preferred  Stock  is  one  taking  preference  of  the 
ordinary  stock  of  a  corporation ;  one  on  which  a  stated  per  cent,  is 
payable  annually,  out  of  net  earnings,  before  any  dividend  can  be 
declared  on  the  common  stock. 

Thus,  the  holders  of  preferred  stock  of  a  certain  railroad  are  entitled  to 
6  per  cent,  on  their  stock  out  of  any  one  year's  earnings,  before  the  common 
stock  can  receive  any  dividend.  After  such  payment,  the  balance  of  earnings, 
if  any  remain,  may  be  divided  to  the  common  stock. 

Preferred  stocks  are  generally  the  result  of  a  reorganization  of  a  railroad. 
For  instance,  the  holders  of  the  common  stock  may  save  the  road  from  passing 
out  of  their  hands  by  the  payment  of  a  certain  sum  of  money,  for  which 
preferred  stock  is  issued.  In  other  cases,  preferred  stocks  have  been  issued 
in  payment  of  floating  or  unsecured  debts. 

In  some  reorganizations,  there  are  two  or  more  classes  of  preferred  stock. 

*  Condensed  from  "  Memoranda  concerning  Government  Bonds,  etc,"  by  Fisk  & 
Hatch,  Bankers,  New  York,  1882. 


STOCKS    AND    BONDS.  217 

461.  A  Bond  is  the  obligation  of  a  Corporation,  City,  County, 
State,  or  Government  to  pay  a  certain  sum  of  money  at  a  certain 
time,  with  a  fixed  rate  of  interest  payable  at  certain  periods,  or, 
as  in  the  case  of  income  bonds,  upon  certain  conditions. 

1.  Bonds  of  business  corporations  are  usually  secured  by  a  mortgage  on 
the  whole  or  some  specified  portion  of  their  property  ;  although  certain  classes 
of  bonds  are  issued  without  mortgage  security,  and  are  dependent  on  the  good 
faith  or  solvency  of  the  company  issuing  them,  having  the  same  force  as  a 
promissory  note. 

2.  Bonds  are  issued   with  coupons  attached  representing  the  different 
installments  of  interest  payable  at  the  different  periods  specified,  during  the 
time  the  bond  has  to  run,  which  are  to  be  cut  off  and  collected  from  time  to 
time  as  the  interest  becomes  due. 

3.  Bonds  are  also  issued  without   coupons,  in   what  is  known1  as  the 
registered  form.     In  this  case  the   bond  is  only  payable  to  the  registered 
owner,  or  his  assignee,  and  the  interest  is  paid  by  check  or  in  cash,  to  the 
owner  or  his  attorney. 

4.  Bonds  are  sometimes  issued  with  coupons  attached  payable  to  bearer, 
but  the  principal  of  which  may  or  may  not  be  registered  at  the  choice  of  the 
owner. 

5.  Bonds  are  known  as  First  Mortgage,  Second  Mortgage,  etc.,  Debentures, 
Consols,  Convertible  Land  Grant,  Sinking  Fund,  Adjustment,  Income  or  other- 
wise, according  to  their  priority  of  lien,  the  class  of  property  upon  which  they 
are  secured,  or  other  characteristics.     Income  bonds  are  generally  bonds  on 
which  the  interest  is  only  payable  if  earned,  and  ordinarily  are  not  secured  by 
a  mortgage. 

Bonds  are  also  named  from  the  rate  of  interest  they  bear,  or  from  the 
dates  at  which  they  are  payable  or  redeemable,  or  from  both ;  as,  U.  S.  4's 
1907,  Virginia  6's,  Western  Union  ?'s,  coupon,  1900,  Lake  Shore  reg.  2d,  1903. 

6.  In  speaking  of  the  income  from  bonds  the  term  "interest"  is  used,  as 
it  is  the  consideration  received  for  the  use  of  money  loaned,  while  that  derived 
from  an  investment  in  stock  is  called  "  dividend,"  because  it  is  money  divided 
to  the  stockholders  from  the  profit  of  carrying  on  the  business,  after  the  fixed 
charges  have  all  been  paid. 

7.  The  bond  of  a  company  may  be  a  perfectly  safe  investment,  when  the 
stock  is  not ;  and  the  stock  of  a  prosperous  and  successful  company,  paying 
large  dividends  or  having  a  large  surplus,  may  sell  at  a  higher  price  than  the 
bonds  of  the  same  company,  the  income  from  which  is  limited  to  the  agreed 
rate  of  interest  which  they  bear.     A  much  closer  scrutiny  should  be  made  of 
a  company's  standing,  when  one  thinks  of  investing  in  its  share  capital,  than 
when  it  is  the  intention  to  loan  the  company  money  on  its  mortgage  bond. 

8.  Convertible  Bonds  are  those  which  are  issued  with  provisions  whereby 
they  can  be  exchanged  for  stock,  lands,  or  other  property. 

9.  Bonds  are  issued  in  denominations  of  $50  to  $50000. 


218 


STOCKS    AND    BONDS. 


GOVERNMENT     BONDS. 

462.  Statement  of  the  Public  Debt  of  the  United  States, 
January  1,  1882. 


INTEREST-BEARING  DEBT. 
Bonds  at  6£,  continued  at  3X#- 
Bonds  at  5£,  continued  at  %%%. 
Bonds  at  ±%%. 
Bonds  at  4%. 
Refunding  Certificates  (4#). 
Navy-Pension  Fund  (o%}. 

DEBT  ON  WHICH  INTEREST  HAS  CEASED  SINCE  MATURITY. 
DEBT  BEARING  NO  INTEREST. 
Old  Demand  Notes,      ....               59,920.00 
Legal-Tender  Notes.    (See  Art.  189.)       346,681,016.00 
Certificates  of  Deposit,        .        .        .          9,590,000.00 
Gold  Certificates,          ....          5,188,120.00 
Silver  Certificates.     (See  Art.  186.)        68,675,230,00 
Fractional  Currency,*          .        .        .          7,075,926.92 

Principal. 

Interest. 

$149,682,900.00 
401,503,900.00 
250,000,000.00 
738,772,550.00 
575,250.00 
14,000,000.00 

$2,619,448.11 
2,379,103.91 
1,394,299.62 
8,149,645.31 
61,880.90 
210,000.00 

1,554,534,600.00 
11,528,265.26 

437,270,212.92 

14,814,378.85 
714,985.31 

7,256.51 

Unclaimed  Pacific  Railroad  Interest. 

TOTAL  DEBT. 
TOTAL  CASH  IN  THE  TREASURY. 

DEBT,  LESS  CASH  IN  THE  TREASURY,  JAN. 

1,  1882. 

2,003,333,078.18 

15,536,619.67 
2,003,333,078.18 

2,018,869,697.85 
253,377,980.76 
1.765,491,717.09 

BONDS  ISSUED  TO  THE  PACIFIC  RAILWAY  COMPANIES,  INTEREST  PAY- 
ABLE BY  THE  UNITED  STATES. 

Principal  outstanding $64,623,512.00 

Interest  accrued  and  not  yet  paid, 1,938,705.36 

Interest  paid  by  the  United  States 51,467^272.02 

Interest  repaid  by  transportation  of  mails,        $14,707,886.34 

By  cash,  payments  5fc  net  earnings,        .                655,198.87  15,363,085.21 

Balance  of  interest  paid  by  the  United  States,       !       ~        '.  36,104,186.81 

463.  The  quotations  of  government  bonds  at  the  New  York 
Stock  Exchange  were  as  follows,  Jan.  3, 1882 : 

Bid.        Asked.  Bid.  Asked. 


Sixes 

continued 

101* 

101* 

U. 

S. 

cur. 

6' 

s; 

1895 

126 



Fives 

continued 

102* 

102J 

U. 

S. 

cur. 

G 

s, 

1896 

127 



U.S. 

4J's,  '91  reg. 

114| 

114-f 

U. 

s. 

cur. 

6s 

s, 

1897 

128 



U.S. 

4%  '91  c. 

114| 

114* 

u. 

s. 

cur. 

6' 

s, 

1898 

129 



U.S. 

4's,  1907  reg. 

117| 

117| 

u. 

s. 

cur. 

6's, 

1899 

130 



U.S. 

4's,  1907  c. 

117* 

117* 

Dist. 

of  Col. 

3-65's 

107 

108 

*  Amount  of  fractional  currency  estimated  as  lost  or  destroyed,  $8,375,934. 


GOVERNMENT   B  ONDS.  219 

All  Government  Bonds  are  dealt  in  and  quoted  "  flat " — that  is  to  say,  the 
quoted  market  price  is  for  the  bond  as  it  stands  at  the  time,  including  the 
accrued  interest — except  that  after  the  closing  of  the  transfer  books*  the 
registered  bonds  are  quoted  ex-interest — that  is  to  say,  the  interest  then  com- 
ing due  belongs  to  the  holder  of  the  bond  at  the  time  of  the  closing  of  the 
books,  and  does  not  go  with  the  bond  to  the  purchaser. 

In  comparing  the  prices  of  the  coupon  and  registered  bonds  during  the  pe- 
riod in  which  the  transfer  books  remain  closed,  it  should  be  remembered  that 
during  that  time  the  quoted  price  of  the  coupon  bonds  includes  the  accrued 
interest  falling  due  on  the  first  of  the  ensuing  month,  while  that  of  the 
registered  bonds  does  not.  If,  in  the  month  of  December,  when  the  books 
are  closed  preparatory  to  the  payment  of  the  interest  due  January  1,  the 
coupon  Four  per  cents  are  quoted  at  118,  the  equivalent  for  the  registered 
bonds  of  the  same  issue  would  be  117,  the  three  months'  interest  being  equal 
to  one  per  cent. 

464.  Continued  6's,  6's  of  1881.     Authorized  by  Acts  of 
July  17  and  August  5,  1861,  and  March  3,  1863.      Eedeemable  at 
the  option  of  the  government  after  June  30,  1881.     During  the 
year  1881,  at  the  request  of  the  holders,  these  bonds  were  continued 
at  Stj-  per  cent.      The   amount   outstanding  Jan.   1,  1882,  was 
$149,682,900,    all   registered.      Interest   is   payable  Jan.   1,   and 
July  1.     Although  these  bonds  can  be  called   at  any  time,  the 
interest  ceasing  at  the    date  of  the  call,  it  is  the  custom  of  the 
Secretary  of  the  Treasury  to  give  60  days'  notice. 

465.  Continued  5's,5's  of  1881.    These  bonds  were  author- 
ized by  the  "Funding  Acts  "  of  July  14,  1870  and  Jan.  20,  1871, 
and  were  issued  for  the  purpose  of  funding  the  5-20  and  10-40 
bonds.     Redeemable  at  the  option  of  the  Government  after  10 
years  from  their  date,  or  after  May  1,  1881.    During  the  year  1881, 
at  the  request  of  the  holders  these  bonds  were  continued  at  #|  per 
cent.     The  amount  outstanding  Jan.   1,  1882,  was  $401,503,900, 
all  registered.      Interest  is  payable  Feb.  1,  May  1,  Aug.  1,  and 
Nov.  1.     These  bonds  may  be  called  at  any  time,  but  the  interest 
will  not  cease  till  three  months  after  the  date  of  the  call. 

466.  4£'s  of  1 89 1 .     Authorized  by  the  Acts  of  July  14, 1870, 
and  Jan.  20,  1871,  and  issued  for  the  purpose  of  funding  the  5-20 
and  10-40  bonds.     Eedeemable  at  the  option  of  the  Government 

*  The  transfer  books  of  U.  S.  registered  bonds  are  closed  for  the  month  preceding  the 
day  on  which  the  interest  is  paid. 


220  STOCKS    AND    BONDS. 

after  15  years  from  their  date,  or  after  Sept.  1, 1891.  The  amount 
outstanding  Jan.  1,  1882,  was  $250,000,000,  of  which  1181,486,000 
were  registered  and  $68,514,000  coupon  bonds.  Interest  is  payable 
Mar.  1,  June  1,  Sept.  1,  and  Dec.  1. 

467.  4's  of  1907.     Authorized  by  the  Acts  of  July  14,  1870, 
and  Jan.  20,  1871,  and  issued  for  the  purpose  of  funding  the  5-20 
and  10-40  bonds.     Redeemable  at  the  option  of  the  Government 
after  30  years  from  their  date,  or  after  July  1,  1907.     The  amount 
outstanding  Jan.  1,  1882,  was  $738,772,550,  of  which  8547,760,700 
were  registered,  and  $191,011,850  coupon  bonds.     Interest  is  pay- 
able Jan.  1,  Apr.  1,  July  1,  and  Oct.  1. 

468.  Refunding  Certificates,    Authorized  by  Act  of  Feb. 
26,  1879.     These  certificates  are  of  the  denomination  of  $10,  bear 
interest  at  4%,  and  are  convertible  at  any  time,  with  accrued  inter- 
est, into  4:%  bonds.     The  amount  outstanding  Jan.  1,  1882,  was 
$575,250. 

469.  Currency  6's.     These  bonds  were  issued  to  aid  in  the 
construction  of  the  Pacific  railroads,  and  were  authorized  by  the 
Acts  of  July  1,  1862,  and  July  2,  1864.     Principal  and  interest  are 
payable  in  lawful  money  of  the  United  States.     Payable  30  years 
after  date,  and  maturing  at  different  dates  from  1895  to  1899. 
The    amount    outstanding   Jan.    1,   1882,   was    $64,623,512,   all 
registered. 

470.  Denominations.     The  coupon  bonds  of  the  various 
issues  are  in  denominations  of  $50,  $100,  $500,  and  $1000.     The 
registered  bonds  are  in  denominations  of  $50,  $100,  $500,  $1000, 
$5000,  and  $10000.     Of  the  funded  loans,  viz.,  the  5's  of  1881,  the 
4£'s  of  1891,  and  the  4's  of  1907,  there  are,  in  addition  to  the 
above,   registered  bonds  of  the  denominations  of   $20,000   and 
$50,000. 

471.  All  the  issues  of  U.  S.  bonds  now  outstanding  are  ex- 
empt from  taxation,  and  with  the  exception  of  the  Currency  6's, 
are  payable  in  coin. 

472.  Coupon  bonds,  being  payable  to  bearer,  pass  by  delivery 
without  assignment,  and  are  therefore  more  convenient  for  sale 


NEW    YORK    STOCK    EXCHANGE.  221 

and  delivery  than  registered  bonds,  which  must  be  assigned  by  the 
party  in  whose  name  they  are  registered.  The  interest  coupons 
being  also  payable  to  the  bearer  will  be  cashed  by  any  bank  or 
banker  in  any  part  of  the  United  States. 

1.  The  interest  on  registered  bonds  is  paid  by  checks,  made  to  the  order 
of  the  registered  owner  and  sent  to  him  by  mail.     These  checks,  when  prop- 
erly endorsed,  can  be  collected  and  cashed  through  any  bank  or  banker. 

2.  Coupon  bonds  may  be  converted  into  registered  bonds  of  the  same 
issue,  but  there  is  no  provision  of  law  for  converting  registered  bonds  into 
coupon  bonds. 

3.  Coupon  bonds  forwarded  to  the  Treasury  Department  for  conversion 
into  registered  bonds  should  be  addressed  to  "  The  Secretary  of  the  Treasury, 
Washington,  D.  C." 

4.  Registered  bonds  forwarded  to  the  Treasury  Department  for  transfer, 
and  requests  for  a  change  in  the  address  to  which  interest  checks  are  to  be 
sent,  should  be  addressed  to  the  "  Register  of  the  Treasury,  Washington,  D.C." 


NEW     YORK     STOCK     EXCHANGE. 

473.  The  New  York  Stock  Exchange  is  an  incorporated 
body  of  brokers,  whose  business  it  is  to  buy  and  sell  stocks,  bonds, 
and  other  representatives  of  value. 

1.  The  present  number  of  members  is  eleven  hundred,  the  maximum 
allowed  under  the  by-laws.     Therefore,  membership  is  only  to  be  obtained 
by  the  purchase  of  the  seat  of  a  deceased  or  retiring  member.     Seats  have 
been  sold  within  the  last  few  mouths  (1882),  for  from  $26000  to  $31000. 

2.  The  floor  of  the  Exchange  is  open  for  business  from  10  A.  M.  to  3  P.  M. 
There  are  two  regular  calls  of  Stocks  daily;  three  of  State  and  Railroad 
Bonds  ;  and  three  of  United  States  Bonds.     Transactions  are  not,  however, 
confined  to  the  regular  calls,  but  are  continually  taking  place  on  the  floor  of 
the  Exchange  between  the  hours  named  above. 

3.  In  Wall  Street,  there  are  what  are  known  as  strictly  commission 
houses,  who  take  and  execute  orders  for  securities,  charging  the  regular  com- 
mission, and,  when  customers  desire,  loaning  funds  on  the  securities  on  a 
deposit  of  10  to  20%  of  market  value  being  made.     This  is  what  is  known  as 
buying  on  a  margin  (478),  where  the  customer  intends  to  sell  soon  again, 
and  merely  buys  for  speculative  purposes.     Such  houses  will  usually  sell 
stocks  "short"  (48O,  11)  for  their  customers  on  a  similar  margin. 

There  are  other  houses  which  make  no  advances,  and  require  customers 
to  pay  outright  for  securities  when  bought. 


222  STOCKS    AND    BONDS. 

Then,  again,  there  are  houses  which  combine  a  banking  and  brokerage 
business,  taking  deposits  and  loaning  money  on  any  securities  marketable  at 
the  Exchange,  and  buying  and  selling  stocks  on  commission.  Some  of  these 
extend  the  privilege  of  marginal  business  to  their  customers,  while  others 
do  not. 

There  are  other  members  and  firms  who  operate  exclusively  for  their  own 
account. 

474.  Quotations  are  made  at  so  much  per  cent,  on  the  basis 
of  a  par  value  of  $100  per  share  of  stock,  except  in  the  case  of 
mining  securities  and  Sutro  Tunnel  stock,  which  are  quoted  at  so 
much  per  share,  without  reference  to  their  par  value. 

For  example,  the  par  value  of  Morris  and  Essex  stock  is  $50,  but  the 
quotation,  if  the  stock  were  worth  just  par  in  the  market,  would  be  100%  ;  or, 
if  the  quotation  is  110,  it  means  $110  for  $100  worth  of  the  par  value,  which, 
in  the  case  of  this  stock,  would  be  two  shares,  while  in  the  case  of  a  stock  the 
par  value  of  which  is  $100  per  share,  it  would  be  for  one  share. 

On  the  other  hand,  if  Sutro  Tunnel,  the  par  value  of  which  is  $10  per 
share,  is  quoted  at  2,  it  means  $2  per  share  ;  and,  in  like  manner,  if  Homestake, 
the  par  value  of  which  is  $100,  is  quoted  at  80,  it  means  $30  per  share. 

475.  Commission.      The   regular  charge  for  buying  and 
selling  securities  dealt  in  at  the  Stock  Exchange,  except  mining 
stocks,  is  one-eighth  of  one  per  cent  (\%}  on  par  value,  or  812.50 
on  100  shares  of  stock  of  the  par  value  of  $100  each. 

1.  The  commission  on  mining  stocks  varies  with  the  market  value  of  the 
stock.     At  present  (1882),  the  rates  charged  at  the  Stock  Exchange,  on  the 
mining  stocks  dealt  in  there,  are  as  follows : 

On  Mining  Stocks  selling  in  the  market  at  not  over  $5 

per  share, $3. 12£  per  100  shares. 

On  shares  selling  at  not  over  $10  and  above  $5  per  share,  6.25      "    100      " 

On  shares  selling  above  $10  per  share, 12.50     "    100      " 

2.  At  the  New  York  Mining  Stock  Exchange,  where  a  large  number  of 
mining  stocks  not  quoted  at  the  Stock  Exchange  are  dealt  in,  the  regular  scale 
of  commissions  is  as  follows  : 

Stocks  selling  under  50  cents  per  share,  .     .    Com.  of  50  cents  per  1 00  shares. 

"      at  50  cts.  and  under  $1  per  share,      "  $1.00  "100  " 

$1              «           $2      "  "  2.00  "  100 

2              "             5      "  "  3.00  "  100  " 

5                          10      "  "  5.00  "  100  " 

10              "           20      "  "  6.25  "  100  " 

20  and  over  per  share,  "  12.50  "   100  " 


NEW    YORK    STOCK   EXCHANGE.  223 

476.  Stocks   are   usually  bought   and   sold   either    "  cash/' 
"regular  way,"  "seller. three"  or  "  buyer  three."    A  stock  sold 
"  cash  "  is  deliverable  the  day  sold  ;  a  stock  sold  "  regular  way  "  is 
deliverable  the  next  day,  or  bought  "  regular  way  "  is  to  be  paid  for 
the  next  day.     Where  nothing  else  is  specified,  "regular  way"  is 
always  understood.     When  a  stock  is  reported  as  bought  "  seller 
three,"  it  is  meant  that  the  seller  of  the  stock  can  deliver  it  on 
either  of  the  three  days  at  his  option,  but  is  not  required  to  deliver 
until  the  third  day.     On  the  other  hand,  when  a  transaction  is 
made  "buyer  three,"  the  buyer  can  demand  delivery  of  the  stock 
at  any  time  within  three  days,  but  must  take  it  and  pay  for  it  by 
the  third  day. 

Transactions  on  any  of  the  above  terms  carry  no  interest. 

If  the  option  is  over  three  days,  six  per  cent,  on  the  selling 
value  of  the  stock  is  paid  by  buyer  to  seller. 

One  day's  notice  is  required  of  intention  to  terminate  an  option 
of  a  longer  period  than  three  days. 

The  Stock  Exchange  does  not  recognize  any  contract  for  over 
sixty  days.  Should  a  stock  pay  a  dividend  during  the  pendency 
of  a  contract,  the  dividend  belongs  to  the  purchaser  of  the  stock, 
unless  otherwise  previously  agreed. 

477.  There  are  two  lists  of  securities  admitted  to  dealings  at 
the  Stock  Exchange,  viz.:     (1)   That  which  is  regularly  called 
every  day  ;  (2)  that  which  is  only  called  at  request.     The  first  list 
is  known  as  the  regular  list,  and  the  second  as  the  free  list. 

478.  A  Margin  is  a  deposit  made  with  a  broker,  by  a  person 
who  wishes  to  buy  or  sell  stock  for  speculation  to  enable  the 
broker  to  "carry"  the  stock  and  protect  himself  against  loss.     It 
is  usually  10$  of  the  par  value  of  the  stock. 

1.  A  person  desiring  to  speculate  in  stocks,  deposits  with  his  broker  $1000 
as  a  margin,  and  directs  him  to  purchase  100  shares  of  a  certain  stock  at  90. 
The  broker  would  pay  for  the  stock  $9000,  $1000  of  which  being  furnished 
by  the  speculator,  and  the  remainder,  $8000,   by  the  broker.     The  broker 
charges  legal  interest  on  the  amount  furnished  by  him  for  "carrying"  the 
stock.    (See  Ex.  54,  Art.  481.) 

2.  The  margin  deposited  with  the  broker  is  simply  to  protect  the  broker 
against  losing  any  money   should  the   stock  move  in  the  wrong  direction. 
In  case  of  its  so  doing,  the  margin  must  be  made  goo:l  by  the  deposit  of  an 
additional  amount,  otherwise  the  broker  will  sell  the  stock  to  protect  himself 
from  losing  any  of  the  money  he  has  advanced. 


224  STOCKS    AND    BONDS. 

479.  A  Stock  Privilege  is  a  contract  by  which  the  maker 
of  the  same  engages  to  purchase,  or  to  sell  to,  the  bearer  thereof,  a 
stated  number  of  shares  of  some  particular  stock,  at  a  certain  price, 
at  any  time  at  the  buyer's  option  within  a  certain  period. 

Stock  Privileges  are  of  four  kinds,  viz. :  Puts,  Calls,  Spreads, 
and  Straddles.  Stock  Privileges  are  not  dealt  in  at  the  Stock 
Exchange. 

1.  A  Call  is  a  contract  by  wliicb  the  holder  is  entitled  to  call  upon  the 
seller  of  the  privilege  for  a  certain  number  of  shares  of  a  stock  at  a  certain 
price,  at  any  time  within  a  certain  period. 

EXAMPLE  OF  A  CALL. 

NEW  YORK,  188 

For  value  received  the  bearer  may  call  on  the  undersigned  for  One 
Hundred  Shares  of  the  stock  of  the  New  Jersey  Central  R.  R.  Co.,  at  eighty- 
eight  per  cent,  of  its  par  value,  at  any  time  within  thirty  days  from  this 
date.  The  holder  of  this  contract  is  entitled  to  all  regular  or  extra  dividends 
declared  during  this  time. 

(Signed) 

Calls  are  purchased  when  an  advance  in  the  price  of  the  stock  is  antici- 
pated, and  can  only  be  procured  at  a  certain  distance  (from  2  to  5%)  above  the 
market  price. 

The  usual  cost  of  Calls  and  Puts  is  1  %  of  the  par  value  of  the  stock,  plus 
a  commission  of  ^  %  • 

Suppose  that  the  market  price  of  N.  J.  C.  R.  R.  stock  is  85,  and  the  above 
call  is  purchased  at  the  contract  price  of  88  (3%  above  the  market).  If,  at 
any  time  during  the  term  of  the  privilege,  the  stock  advances  to  92,  and  the 
contract  is  closed,  the  transaction  would  show  a  profit  as  follows  : 

100  shares  N.  J.  C.  R.  R.,  market  value  92,        ....        $9200.00 
100      "  "  as  per  the  Call,          ....          8800. 

400. 

Less  cost  of  Privilege  $100  +  TV%  of  par  value,    .         .     $106.25 
Commission  for  selling  stock  \% ,           ....         12.50  118.75 

Net  profit, 281.25 

If  the  stock  had  declined,  or  had  not  advanced  to  88,  the  contract  price, 
the  operator  would  have  lost  the  cost  of  the  call,  or  $10(5.25. 

2.  A  Put  is  a  contract  by  which  the  holder  is  entitled  to  put  or  deliver  to 
the  seller  of  the  privilege  a  certain  number  of  shares  of  a  stock  at  a  certain 
price,  at  any  time  within  a  certain  period. 


NEW    YORK   STOCK    EXCHANGE.  225 


EXAMPLE  OE  A  PUT. 

NEW  YORK, 188 

For  value  received  the  bearer  may  deliver  to  the  undersigned  One  Hun- 
dred Shares  of  the  Chicago  and  Northwestern  R.  R.  Co.  Preferred  Stock,  at  185 
per  cent,  of  its  par  value,  at  any  time  within  thirty  days  from  this  date. 
The  undersigned  is  entitled  to  all  regular  or  extra  dividends  declared  during 

this  time. 

(Signed) „ 

A  Put  is  the  reverse  of  a  Call  and  becomes  of  value  to  the  holder  when 
there  is  a  decline  in  the  market.  The  contract  price  is  from  2  to  5  per  cent, 
below  the  market  price  of  the  stock. 

3.  A  Spread,  or  Double  Privilege  is  a  combination  of  a  Put  and  a  Call. 

4.  A  Straddle  is  a  Spread,  or  Double  Privilege,  issued  at  the  market  price, 
instead  of  at  a  distance  on  each  side  of  the  market. 

48O.  Explanation  of  Words  and  Phrases  used  in  Wall  Street. 

1.  Bear.  An  operator  who  is  "  short "  of  stock.     He  wishes  to  buy  at  a 
lower  rate,  and  therefore  tries  to  depress  the  price  of  the  stock  of  which  he  is 
"  short." 

2.  Bull.  An  operator  who  is  holding  stock  for  an  advance.  He  is  said  to  be 
"  long  "  of  the  stock.     Bulls  try  to  advance  the  prices  of  the  stocks  of  which 
they  are  "long." 

8.  b.  3  (Buyer  3\  10,  20,  30,  etc.  Meaning  at  the  buyer's  option,  within 
three  days,  ten  days,  etc.  When  in  a  stock  transaction,  the  buyer  has  the 
privilege  of  taking  the  stock  at  any  time  during  the  number  of  days  mentioned. 
In  buyer's  options,  when  the  option  is  for  more  than  three  days,  six  per  cent, 
interest  is  charged  the  buyer,  and  the  seller  is  entitled  to  one  day's  notice. 

4.  b.  c.,  "  between  calls."     The  sale  not  taking  place  on  the  call  of  the 
stock,  but  after  the  first  call  and  before  the  second. 

5.  Collaterals.     Stocks,  bonds,  notes,  or  other  value  given  in  pledge  as 
security,  when  money  is  borrowed. 

6.  Cover,  to  "cover  one's  shorts."      Where  stock   has  been  sold  short, 
and  the  seller  buys  it  in  to  realize  his  profit,  or  to  protect  himself  from  loss, 
or  to  make  his  delivery.     This  is  "  covering  short  sales." 

7.  Differences.     When  the  price  at  which  a  stock  is  bargained  for  and 
the  rate  on  day  of  delivery  are  not  the  same,  the  broker  against  whom  the 
variation  exists,  frequently  pays  the  "difference"  in  money,  instead  of  fur- 
nishing or  receiving  the  stock. 


226  STOCKS    AND    BONDS. 

8.  Ex-Div.,  Ex- Dividend.     When  the  price  or  quotation  of  a  stock  does 
not  include,  and  the  stock  does  not  carry  to  the  buyer  a  recently  declared 
dividend. 

9.  Hypothecating.     Putting  up  collaterals. 

10.  Seller,  3,  10,  20,  30,  etc.     Sold  deliverable  at  seller's  option,  within  the 
number  of  days  named.     When  seller's  options  are  for  more  than  three  days, 
the  buyer  pays  six  per  cent,  interest,  unless  "  flat "  is  specified  in  the  contract, 
and  the  seller  must  give  one  day's  notice  of  delivery. 

11.  S1u>rt.     When  one  has  sold  stock  which  he  does  not  own,  hoping  to 
realize  a  profit  by  buying  in  at  lower  prices,  he  is  said  to  be  "  short." 

12.  Syndicate.     A  combination  of  bankers  who  together  undertake  the 
placing  of  a  loan. 

13.  Watering  a  Stock.     The  act  of  increasing  the  quantity  of  a  stock 
without  a  corresponding  increase  in  the  value  of  the  property  which  it  repre- 
sents.    This  is  usually  done  in  the  reorganization  of  a  railroad,  or  in  the 
consolidation  of  two  or  more  railroads. 

EXAM  PLES. 

481.  1.  A  bank  with  a  capital  (459)  of  $250,000,  declares 
a  semi-annual  dividend  of  3J$.  What  is  the  amount  of  the  divi- 
dend, and  how  much  will  a  stockholder  receive  who  owns  16  shares 
of  $100  each  (459,  1)  ? 

2.  An    insurance   company   divides    among    its   stockholders 
$18000.     What  is  the  rate  of  the  dividend,  the  capital  stock  being 
$225000  ?     How  much  is  paid  to  Mr.  A.,  who  has  a  certificate 
(459,  2)  for  25  shares  ? 

3.  A  gas  company  declares  a  dividend  of  5%,  and  divides  among 
its  stockholders  $125000.     What  is  its  capital  stock  ? 

4.  The  board  of  directors  of  a  mining  company  declared  a  divi- 
dend of  $100,000,  being  five  cents  per  share  (par  value  $10)  on 
the  capital  stock  of  the  company.     What  was  the  capital  stock, 
and  in  how  many  shares  was  it  divided  ?     The  dividend  was  what 
per  cent,  of  the  capital  stock  ? 

5.  An  installment  of  10$  was  assessed  and  called  on  the  capital 
stock  of  a  new  railroad  company.     How  much  was  paid  by  Mr.  B. 
who  had  subscribed  for  50  shares  (par  value  $100)  ? 

6.  A  railway  company,   whose   capital   stock   is   $1,750,000, 
declares  a  dividend  of  3£  per  cent.     What  was  the  amount  of  the 
dividend  ? 


STOCKS    AND    BONDS.  227 

7.  The  Union  Pacific  Railway  paid  to  its  stockholders,  in  1879? 
$2,204,700.     What  was  the  par  value  of  its  stock,  the  rate  of  the 
dividend  being  6%  ? 

8.  A  quarterly  dividend  of  3|%  was  declared  by  a  manufactur- 
ing company.     What  was  the  capital  stock,  the   amount   of  the 
dividend  being  $2100  ? 

9.  If  stock  is  quoted  at  116-f,  what  is  the  market  value  of  200 
shares  ? 

10.  How  many  shares  of  W.  U.  Tel.  can  be  bought  for  $43725 
at  79-f,  brokerage  \%? 

11.  What  is  the  total  par  value  (459,  3)  and  the  total  market 
value  of  100  shares  Lake  Shore  at  118-f  (474),  300  sh.   N.  J. 
Central  at  89f,  500  sh.  W.  U.  Telegraph  at  78$,  200  sh.  U.  S. 
Express  at  73},  and  500  sh.  N.  Y.,  L.  E.  &  W.  com.  at  40$,  and 
800  sh.  K  Y.,  L.  E.  &  W.  pref.  (46O)  at  90$  ? 

12.  What  is  the  cost  of  250  shares  Tex.  &  Pac.  at  50-f  and  100 
shares  Ohio  &  Miss.  pref.  at  104,  brokerage  \%  (475)  ? 

13.  What  are  the  proceeds  of  600  shares  Morris  and  Essex  (half 
stock,  459,  1)  sold  through  a  broker  at  121J  ? 

14-  What  are  the  proceeds  of  the  following  stocks  sold  through 
a  broker?  200  shares  Union  Pacific  at  117$,  2000  shares  K  Y., 
0.  &  W.  at  27},  800  shares  A.  &  T.  H.  pref.  at  88,  and  600  shares 
Chi.  &  Alton  at  131}. 

15.  Find  the  cost  of  10  shares  Manhattan  Bank  at  135,  $5000 
Erie  7's  (461,  5)  cons,  gold  bonds  (461)  at  128,  $1000  Toledo 
and  Wabash  2d,  s.  3  (461,  5— 480, 10)  at  108$,  $5000  C.  R.  I.  &  P. 
6's,  1907,  coupon  (461,  2)  at  129,  and  $5000  Ohio  Southern  Income 
(461,  5)  at  45,  usual  brokerage. 

16.  Find  the  proceeds  of  $15000  U.  S.  4's,  registered,  1907 
(467),  b.  3,  at  117£,  and  $10000  U.   S.  4fs  coupon  (466)  at 
114|-,  usual  brokerage. 

17.  How  much  must  be  invested  in  U.  S.  4£'s,  1891,  to  produce 
a  quarterly  income  of  $675,  bonds  selling  at  114$  ? 

18.  When  Ohio  6's,  1886,  are  sold  at  109J,  what  is  received  for 
six  $500  bonds,  brokerage  }%  ? 

19.  When  Pittsburg,  Fort  Wayne  and  Chicago  2d  7's,  1912,  are 
worth  135,  what  will  $12000  in  bonds  cost  ? 

20.  How  many  $500  bonds  shall  I  receive  for  $4735  invested 
in  U.  S.  4's  at  118$  ? 


«28  STOCKS    AND    BONDS. 

<\ 

k    21.  How  much  must  be  sent  to  a  broker  that  he  may  purchase 
$8000  U.  S.  continued  fives  (465)  at  102f ,  commission  \%  ? 

22.  An  executor  sold  Central  of  New  Jersey  stock  at  52-f,  and 
purchased  with  the  proceeds  $42000  in  U.  S.  4's,  1907,  at  100 •}. 
What  was  the  par  value  of  the  stock  sold,  usual  brokerage  ? 

23.  A  broker  bought  on  his  own  account  200  sh.  Nor.  Pac.  pf. 
at  69-},  and  sold  the  same  the  same  day  at  73|.     What  was  his 
gain? 

24.  How  many  shares  of  111.  Cen.  bought  at  129-f  and  sold  at 
132f,  usual  brokerage,  will  produce  a  gain  of  $1375  ? 

25.  What  income  will  be  produced  by  investing  $235250  in  4% 
bonds  at  117|  ? 

26.  The  common  stock  of  a  railroad  company  is  $46,000,000, 
and  the  preferred  stock  (46O)  $8,000,000.    The  company  declares 
a  dividend  of  3%%  on  the  preferred  stock,  and  %%  on  the  common 
stock.     What  is  the  surplus,  if  the  net  earnings  are  $1,317,645? 

27.  Bought  June  4,  800  sh.  Ohio  &  Miss.  pref.  at  35J,  s.  30. 
The  stock  was  delivered  June  24.     What  was  the  amount  paid 
including  interest  (48O,  10)  ? 

28.  Bought  May  16,  200  sh.  Lake  Shore  at  116},  b.  60,  and 
called  for  the  stock  July  5.     What  was  the  cost  including  interest 
(48O,  3)  ? 

29.  Jan.  10,  sold  100  sh.  Phil.  &  Eead.  at  65J-,  s.  3.    Jan.  13,  the 
stock  was  quoted  at  68-J.     How  much  was  the  difference  (48O,  7) 
paid  by  the  seller  in  settlement  ? 

30.  What  was  the  cost,  including  commission  (475,  2)  at  the 
N.  Y.  Mining  Stock  Exchange  of  500  sh.  (par  value  $10)  mining 
stocks  at  7.50  ?  What  would  have  been  the  total  cost,  if  bought 
at  the  N.  Y.  Stock  Exchange  (475,  1)  ? 

31.  The  transactions   of  the  United  States  in  refunding  the 
Public  Debt  from  Mar.  1,  1877  to  Oct.  1,  1879  were  as  follows  :— 
Loan  of  1858,  5's,  $260,000;  ten-forties  of  1864,  5's,  $193,890,250  ; 
five-twenties   of   1865,  6's,   $100,436,050;    consols  of   1865,   6's, 
$202,663,100  ;  consols  of  1867,  6's,  $310,622,750  ;   consols  of  1868 
6's,  $37,473,800.     In  place  of  the  above  bonds  there  were  issued 
the  following :— Funded  loan  of  1891,  4|'s,  $135,000,000;  funded 
loan  of  1907,  including  certificates,  4's,  $710,  345,950.     What  was 
the  total  amount  refunded,  and  what  was  the  annual  saving  in 
interest  ? 


STOCKS    AND    BONDS.  229 

32.  Sept.  1,  1865,  the  interest-bearing  debt  of  the  United 
States  was  as  follows  :  4  per  cents.,  $618,127.98 ;  5  per  cents., 
$269,175,727.65;  6  per  cents.,  $1,281,736,439.33;  7^  per  cents., 
$830,000.00.  What  was  the  total  annual  interest  charge  ? 
*  33.  The  interest-bearing  debt  of  the  United  States  was  as  fol- 
lows, Jan.  1,  1881:  6's,  $202,266,550;  5's,  $469,651,050;  4J's, 
$250,000,000;  4's,  $739,347,800;  3's,  $14,000,000.  What  was 
the  decrease  during  the  year  1881  in  the  annual  interest  charge  ? 
(See  statement  of  Jan.  1,  1882,  Art.  463.)  What  was  the  inter- 
est of  the  debt  for  one  day  (-^JT  yr.)  Jan.  1,  1882  ? 

34.  The  population  of  the  United  States  and  Territories  Jan.  1, 
1881,  was  50,152,554,  and  the  public  debt  was  $1,899,181,735. 
What  was  the  debt  per  capita  ?     What  was  the  average  monthly 
decrease  of  the  debt  during  the  year  1881  ?     (See  statement,  Art. 
462.) 

35.  The  interest-bearing  debt  of  the  United  States  was  as  fol- 
lows, Dec.  1,  1881 :  Continued  6's  (3|'s)  (464),  $159,452,500,  last 
interest  paid  July  1 ;  continued  5's  (3J's)  (465),  $401,504,900,  last 
interest  paid  Nov.l  ;  4J's  (466),  $250.000,000,  last  interest  paid 
Sept.  1  ;  4's  (467),  $739,347,800,  last  interest  paid  Oct.  1 ;  navy 
pension  fund  (3's),  $14,000,000,  last  interest  paid  July  1.     What 
was  the  aggregate  of  the  interest-bearing  debt,  and  the  accrued 
interest,  Dec.  1,  1881  ? 

36.  The  gross  earnings  (including  the  Omaha  bridge)  of  the 
Union   Pacific  Eailway  Co.  for   1879,  were   $13,201,077.66 ;  the 
operating  expenses  (including  taxes)  were  $5,475,503.44.     What 
were  the  surplus  earnings,  and  what  per  cent,  of  the  gross  earnings 
were  the  operating  expenses  ? 

37.  A  synopsis  of  the  report  of  the  N.  Y.  C.  &  H.  E.  R.  E.  for 
its  fiscal  year  ended  Sept.  30,  1881,  is  as  follows :   Gross  earnings 
from    passengers,  $6,958,038  ;    from   freight,  $20,736,749  ;    from 
miscellaneous,  $4,653,608;  expenses,  $19,464,786;  interest,  rentals, 
and  taxes,  $4,990,783.    What  was  the  surplus  for  the  year  after  the 
declaration  of  a  dividend  of  8%  on  a  capital  stock  of  $89,229,300  ? 
The  expenses  were  what  per  cent,  of  the  total  earnings  ? 

38.  The  L.  S.  &  M.  S.  Railway  reported  as  follows  for  the  year 
ended   Dec.  31,  1880 :    Gross   earnings,   $18,749,461 ;    operating 
expenses  and  taxes,  $10,418,105  ;    interest,  rentals,  dividend  on 
guaranteed  stock,  and  $250,000  for  the  sinking  fund,  $3,000,374, 


230  STOCKS    AND    BONDS. 

After  paying  a  dividend  of  8$,  there  was  a  surplus  for  the  year  of 
81,373,662.  What  was  the  amount  of  the  dividend,  and  the  capi- 
tal stock  ? 

89.  The  gross  earnings  of  the  M.  C.  E.  R.  for  the  year  ended 
Dec.  31,  1880,  were  $9,085,749  ;  operating  expenses  and  taxes, 
$5,738,751;  interest  and  rentals,  $1,586,410.  After  declaring  a 
dividend,  there  was  a  surplus  of  $261,532.  What  was  the  rate  of 
the  dividend,  if  the  amount  of  the  stock  was  $18.738,200  ?  For 
the  year  1881,  a  dividend  of  2£$  was  paid  on  the  same  stock;  what 
was  the  amount  of  the  dividend  ? 

*  40.  The  capital  stock  of  a  railroad  company  was  "watered" 
(48O,  13)  by  declaring  a  stock  dividend  of  10$.  If  the  market 
value  of  the  old  stock  was  110,  what  should  be  the  value  of  the 
new  stock  ? 

>/  41.  Jan.  1,  1882,  the  A.  &  B.  E.  R.,  having  a  capital  stock  of 
$20,000,000,  was  consolidated  with  the  B.  &  C.  E.  E.,  having  a 
capital  stock  of  $32,000,000.  The  new  company  was  organized 
under  the  name  of  the  A.,  B.,  &  C.  E.  E.  For  every  share  of  the 
A.  &  B.  E.  E.  there  was  issued  1 1  shares  of  the  new  stock,  and  for 
every  share  of  the  B.  &  C.  E.  E.  there  was  issued  1£  shares  of  the 
new  stock.  What  was  the  capital  stock  of  the  new  company,  and 
how  much  was  the  stock  "  watered  "  ? 

J4#.  Before  the  consolidation,  the  stock  of  the  A.  &  B.  E.  E. 
was  worth  1.20  in  the  market,  and  the  stock  of  the  B.  &  C.  E.  E., 
90.  What  should  be  the  quotation  of  the  new  stock  ? 

43.  During  the  year  1881,  the  A.  &  B.  E.  E.   divided  among 
its  stockholders  $1,600,000,  and  the  B.  &  C.  E.  E.,  $1,920,000. 
During  the  year  1882,  the  new  company  divided  an  amount  equal 
to  the  total  dividends  of  the  two  companies  in  the  preceding  year. 
What  were  the  rates  of  the  dividends  of  the  two  companies  in  1881, 
and  the  rate  of  the  dividend  of  the  consolidated  company  in  1882  ? 

44.  'Mr.  A.  had  10  shares  of  the  A.  &  B.  E.  E.,  and  16  shares 
of  the  B.  &  C.  E,  E.     What  was  the  total  amount  of  his  dividend 
in  1881  ?     How  many  shares  of  the  new  stock  did  he  receive,  and 
what  was  the  amount  of  his  dividend  in  1882? 

45.  A  gentleman  bought  bank  stock,  paying  regular  annual 
dividends  of  6$,  at  120.     What  was  the  rate,  per  cent,  of  his  in- 
come, or  what  per  cent,  did  he  receive  on  the  money  invested? 


STOCKS    AND    BONDS.  231 

ANALYSIS. — Since  dividends  are  reckoned  on  the  par  value  of  the  stock, 
the  dividend  on  1  share  of  $100  would  be  $6.  Since  each  share  costs  $120,  and 
pays  $6  income,  the  per  cent,  will  be  $6-r-$120,  or  §°/0. 

NOTE. — The  above  analysis  will  not  apply  to  bonds  that  mature  at  a  cer- 
tain fixed  time,  unless  the  investor  expects  to  sell  the  bonds  before  maturity 
at  the  cost  price.  If  6%  bonds  that  mature  in  1891  are  purchased  in  1881  at 
120,  and  are  sold  at  the  same  rate  before  maturity,  they  will  pay  §%  on  the 
investment,  or  cost.  If  the  bonds  are  held  until  maturity  (1891),  or  for  10 
years,  the  owner  would  receive  from  the  government  the  par  value  only,  or 
$100  for  a  bond  of  that  amount,  and  the  bonds  would  yield  less  than  5%. 
If  6%  bonds,  maturing  in  10  years,  are  purchased  at  1.07 j^  and  held  until 
maturity,  they  will  pay  5%  on  the  investment  (See  Ex.  64).  If  Q%  bonds, 
that  mature  in  2  years,  are  purchased  at  more  than  112,  there  would  be  a  loss 
of  interest  to  the  purchaser  instead  of  a  gain. 

46.  Which  is  the  better  investment,  stock  paying  a  regular 
annual  dividend  of  5$  and  bought  at  80,  or  stock  paying  8$ 
dividends  and  bought  at  120  ? 

47.  If  insurance  stock  paying  regular  dividends  of  10$  annually 
is  bought  at  137£,  brokerage  J$,  what  per  cent,  of  income  will  it 
produce  ? 

48.  Which  investment  will  produce,  the  greater  annual  income 
and  how  much,  $20,000  invested  in  Chemical  Bank  stock  at  2000 
which  pays  dividends  of  15$  every  2  months,  or  the  same  amount 
invested  in  Chatham  Bank  stock  at  125  which  pays  regular  semi- 
annual dividends  of  3$  ? 

49.  What  rate  can  you  afford  to  pay  for  stock  paying  regular 
annual  dividends  of  10$,  in  order  to  realize  6$  on  the  invest- 
ment ? 

50.  At  what  price  must  8$  stocks  be  purchased  to  afford  5$  on 
the  investment  ?    To  afford  6$  ? 

51.  Stocks  bought  at  80  pay  regular  dividends  of  5$.     What 
is  the  rate  per  cent,  on  the  investment  ?    At  what  rate  should  they 
be  purchased  to  afford  4$  on  the  investment?     To  afford  8$? 

52.  I  sell  200  sh.  H.  &  St.  J.  pf.  at  lllf,  and  $10000  K  Y. 
Elevated  1st  mortgage  bonds  at  119.     What  will  be  the  net  pro- 
ceeds of  the  sale,  allowing  usual  brokerage  ? 

53.  Purchased  400  shares  Lake  Shore  at  118-J-,  and  200  shares 
Chesapeake  and  Ohio  2d  pref.,  at  24|.     Sold  the  Lake  Shore  at 
113f,  and  the  Chesapeake  and  Ohio  at  22J.     What  was  the  loss, 
usual  brokerage,  no  interest  ? 


STOCKS   AND    BOXDS. 


54-  July  26,  a  broker  received  from  a  customer  a  remittance  of 
$1000  as  a  margin  (478)  and  purchased  for  him  100  shares  of 
St.  Paul  Common  at  59.  On  Aug.  2,  the  broker  sold  the  stock  at 
What  was  the  customer's  profit  ? 


OPERATION. 


Dr. 

July  26. 

To  100  shares  St.  Paul  Com.  59. 
Commission  \% 

.  $5900 
12.50 

5912 

50 

Aug.  2. 

Interest  $5912.50,  7  days. 

• 

* 

** 

*#** 

** 

Cr. 

July  26. 
Aug.  2. 

By  margin  deposited 
"  100  shares  St.  Paul  Com.  64|. 
Commission  \  % 

.  $6450 
12.50 

1000 
6437 

50 

Aug.  2. 

Interest  $1000,  7  days     . 

. 

* 

#* 

**** 

•*# 

Balance. 

*fc## 

~*# 

The  profit  is  equal  to  the  balance  less  $1000,  the  original  deposit. 

55.  Aug.  30,  a  broker  purchased  for  the  account  of  a  customer 
300  shares  Northwestern  Railroad  stock  at  78.     He  deposited  as 
a  margin  $3000.     On  Sept.  22,  the  stock  was  sold  at  74}.     What 
was  the  loss  ?     (Interest  6%,  usual  commission.) 

56.  May  10,  a  speculator  deposited  with  his  broker  $5000  as  a 
margin,  and  directed  him  to  purchase  for  his  account  500  shares 
K".  Y.,  L.  E.,  &  W.,  pref.  at  90|.     May  20,  the  stock  was  sold  at 
94rJ-.     What  was  the  gain,  interest  6$,  usual  brokerage  ? 

57.  Sept.  10,  I  deposited  with  my  broker  $5000  as  a  margin, 
and  he  purchased  for  me  200  sh.  Cen.  Pac.  at  90-J-,  200  sh.  Morris 
&  Essex  (half  stock)  at  122J,  200  sh.  Tex.  &  Pac.  at  49}.     The 
stocks  on  Sept.  30  were  quoted  as  follows:    Cen.  Pac.  80},  Morris 
&   Essex   120-J,  Tex.  &  Pac.    41f.     How   much   should  I  have 
deposited  with  my  broker  to  make  my  margin  of  10%  good,  and 
to  cover  commission  for  buying  and  selling,  and  interest  ?    If  I 
had  been  unable  to  have  made  an  additional  deposit,  and  the  broker 
had  "sold  me  out,"  what  would  have  been  my  loss  ? 

58.  An   operator,    supposing  Erie  would    decline    in   value, 
ordered  his  broker  to   sell  short   100  shares  at  50,  and  at  the 
same  time  deposited  with  him  as  a  margin  $1000.     The  broker 
on  receiving  the  order  sold  for  his  account  100  shares  at  50,  and 
borrowed  the  stock  for  delivery.     When  the  market  price  declined 


STOCKS    AND    BONDS.  233 

to  45,  he  ordered  the  broker  to  "  coyer  his  short  sale  "  (buy  the 
stock  for  delivery),  and  return  the  stock  to  the  party  from  whom 
it  was  borrowed.  What  was  the  gain,  usual  brokerage  ? 

OPERATION. 

Cr. 

By  margin  deposited $****** 

"  100  shares  Erie  borrowed  and  sold  at  50.     .        .          ******        $****.** 

Dr. 

To  100  shares  Erie  bought  and  returned  at  45.         .        $****.** 
"  commission  for  selling  the  stock  \%.  .        .        .  **%*# 

"  buying  and  returning  the  stock  \%.       ^**  .**          ****** 

"  amount  to  credit.          . ' ##**t*» 

The  net  profit  equals  the  balance  less  the  margin  deposited. 

NOTE. — There  is  no  interest  charged  on  short  sales,  but  it  sometimes 
happens  that  a  small  bonus  has  to  be  paid  for  the  use  of  the  borrowed  stock. 

59.  A  broker  sold  "short"  for  me  400  sh.   0.  B.  &  Q.,  at 
135},  and  100  sh.   C.  R.  I.  &  P.,  at  132£.    My  "short"  sale  on 
C.  B.  &  Q.   was  "  covered"  at  131£,  and  C,  R.  I.  &  P.  at  133}. 
What  was  my  net  profit,  usual  brokerage  ?    (No  interest. ) 

60.  Sold  Aug.  11,  500  shares  Chicago  &  Alton,  s.  3,  at  94 J, 
and  covered  my  short  sale  Aug.  14,  at  91.     What  was  my  profit, 
allowing  the  usual  brokerage  ? 

61.  June  16,  bought  a  Call  (479,  1)  on  300  shares  Michigan 
Central  at  86,  for  30  days,  for  which  I  paid  $300.     Called  the 
stock  July  6,  and  sold  it  in  the  market  the  same  day  at  91^. 
What  was  my  gain,  commission  on  call  -fa%9  for  selling  stock  \%> 
interest  Q%? 

NOTE. — Calls  bear  interest  at  6^  from  the  date  of  the  contract  till  the 
contract  is  closed,  but  Puts  do  not. 

62.  If,  in  the  preceding  example,  the  stock  had  not  advanced 
to  86  at  any  time  within  30  days,  what  would  have  been  the  loss  ? 
What  would  have  been  the  result  if  the  stock  had  been  sold  July 
16  at  87 &  and  called  for  delivery?    If  sold  July  1  at  86£  ? 

63.  Sept.  18,  bought  a  Put  (479,  2)  on  400  shares  C.  C.  &  I.  C. 
at  20,  for  30  days,  for  $400.     I  purchased  the  stock  at  16  and 
made  my  delivery  on  the  Put.     What  was  my  gain,  commission 
on  Put  TV%,  on  stock  \%  ?    What  would  have  been  my  loss,  if  the 
stock  had  not  fallen  below  20?     What  would  have   been   the 
result,  if  the  stock  were  purchased  for  delivery  at  18|  ?    At  19J-  ? 


234  STOCKS    AND    BONDS. 

64.  At  what  price  may  Q%  bonds,  maturing  in  10  years,  be 
purchased,  so  that  the  investment  will  pay  b%  ? 

NOTE. — Tables  have  been  constructed  on  various  plans,  and  different 
methods  are  used  by  bankers  and  financiers,  for  the  solution  of  problems 
relating  to  bond  investments;  two  of  which  are  given  below. 

ANALYSIS. — 1.  In  the  following  method,  it  is  presumed  that  the  accruing 
interest  is  not  reinvested,  but  that  a  sufficient  part  of  it  is  set  aside  as  a  sinking 
fund  to  make  up  the  amount  which  was  originally  paid  out  as  premium. 

A  $1000  bond  in  10  years  at  6^  would  amount  to  $1600  ($1000  + 10  x  $60). 
$1  in  10  years  at  5^  would  amount  to  $1.50.  To  amount  to  $1600,  the  prin- 
cipal, or  the  amount  paid  for  the  bond,  must  be  as  many  times  $1  as  $1.50  are 
contained  times  in  $1600,  or  $1066.66f  (106jj-$). 

If  a  $1000  bond  is  purchased  at  108|,  it  will  be  necessary  to  set  aside  as  a 
sinking  fund  each  year  $6.66f  (f%)  to  make  up  the  premium  in  10  years. 
The  annual  interest,  $60,  less  $6|,  the  annual  sinking  fund,  is  $53y,  which  is 
5fo  of  $1066|,  the  cost  of  the  bond  or  the  amount  invested. 

If  the  amount  set  aside  as  a  sinking  fund  is  placed  at  interest,  either 
simple  or  compound,  §%  bonds,  maturing  in  10  years  and  purchased  at  106|, 
would  pay  a  little  more  than  5  % . 

2.  The  following  method  anticipates  compound  interest  throughout  ;  i.  e., 
the  interest  is  immediately  reinvested  at  compound  interest. 

The  holder  of  a  $1000  bond  would  receive  $60  interest  annually,  and 
$1000,  the  face  of  the  bond,  in  10  years.  If  money  is  worth  5%,  the  several 
interests  in  the  10  years  at  compound  interest  would  amount  to  $754.674 
($1  placed  at  compound  interest  at  the  beginning  of  each  year  would 
amount  in  9  years  to  $11.5779  (342).  $11.5779  plus  $1  of  the  last  inter- 
est  =  $12.5779.  $60  would  amount  to  60  times  $12.5779,  or  $754.674). 
$1000,  the  principal,  plus  $754.674,  the  compound  amount  of  the  interest, 
equals  $1754.674,  the  total  value  of  the  bond  at  maturity,  money  being  worth 
5$.  The  present  worth  of  $1754.64,  due  in  10  years,  at  5%  compound  inter- 
est, is  $1754.64  -f- $1.6289  (341),  or  $1077.19.  Hence  the  bonds  must  be 
purchased  at  1.07T7^  to  pay  5%  on  the  investment.  See  Ex.  45,  Note. 

65.  What  must  I  pay  for  6^  bonds,  maturing  in  15  years, 
that  my  investment  may  yield  ty%  ?     (Both  methods.) 

66.  6f0  bonds,  maturing  in  10  years  and  bought  at  106f ,  pay 
what  per  cent,  on  the  investment  ?     (See  1st  analysis,  Ex.  64.) 

ANALYSIS.— A  $1000  bond  would  amount  in  10  years  at  6%  to  $1600.  If 
$1066.66|  is  paid  for  the  bond,  the  net  interest  for  10  years  is  $1600-  $1066  66|, 
or  $533.33| ;  and  for  one  year  $533.33J-;-10,  or  $53.331.  An  income  of  $53.33| 
on  an  investment  of  $1066.66|  is  equivalent  to  5#  ($53.33|-r-$1066.66f). 

67.  What  rate  of  interest  do  I  receive  on  my  investment,  if  I 
buy  7%  bonds  maturing  in  20  years  at  133J? 


TAXES. 


DEFINITIONS. 

482.  A  Tax  is  a  sum   of  money  assessed  on  persons  and 
property  to  defray  the  expenses  of  a  state,  county,  town,  corpo- 
ration, or  district. 

1.  In  certain  states  all  citizens  above  21  years  of  age  are  required  by  law 
to  pay  a  certain  tax  on  the  person.     This  tax  is  called  a  Capitation  or  Poll 
Tax. 

2.  The  expenses  of  states,  counties,  towns,  etc.,  are  paid  by  a  direct  tax 
upon  the  property  or  polls  of  the  same.     The  methods  of  assessing  taxes  differ 
in  the  several  states.     In  some  states,  a  certain  percentage  of  the  whole  tax  is 
assessed  upon  the  polls,  while  in  others  the  poll  tax  is  a  fixed  amount  for  each 
citizen.     In  certain  states,  the  whole  tax  is  paid  by  the  owners  of  the  property 
of  the  same. 

3.  The  expenses  of  the  United  States  government  are  paid  by  duties  on 
imports ;  the  internal  revenue  (the  tax  upon  distilled  spirits,  fermented  liquors, 
tobacco,  snuff,  and  cigars,  proprietary  medicines,  perfumery  and  cosmetics, 
playing  cards,  matches,   etc.) ;   sales  of  public    lands ;   tax  on   circulation, 
deposits,  and  capital  of  national  banks  ;    customs  fees,  fines,  penalties,  and 
forfeitures;  fees,  consular,  letters  patent,  and  land  ;  profits  on  coinage,  etc. 

The  receipts  of  the  United  States  for  the  fiscal  year  ended  June  30, 1881, 
were  as  follows:  Customs  (including  tonnage  dues),  $198,159,676;  internal 
revenue,  $135,264,385;  public  lands,  $2,201,863;  miscellaneous,  $25,156,366. 

483.  Real  Estate  is  fixed  property  ;  as  land,  houses,  etc. 

484.  Personal  Property  is  movable  property,  as  money, 
stocks,  bonds,  mortgages,  furniture,  merchandise,  etc. 

485.  An  Assessor  is  a  person  appointed  or  elected  to  esti- 
mate the  valuation  of  all  property  liable  to  taxation. 

486.  A  Collector  or  Receiver  of  taxes  is  a  person  appointed 
or  elected  to  collect  or  receive  the  taxes  of  a  city,  town,  village,  or 
district. 

Collectors  receive  a  commission  on  the  amount  collected  or  a  fixed  salary. 


236  TAXES. 


EXAM  PLES. 

487.  1.  For  the  fiscal  year  1879,  the  N".  Y.  State  tax  levy 
was  at  the  rate  %-&£$  mills.  How  much  would  this  rate  produce, 
the  valuation  of  the  taxable  property  being  $2,686,140,000  ? 

2.  The  rate  of  taxation  of  a  certain  county  was  3J  mills,  and 
the  amount  of  the  tax  $40,653.48.     What  was  the  valuation  of  the 
property  ? 

3.  The  following  were  the  rate&  of  taxation  of  New  York  for 
state  purposes,  1880  :  —  schools,  •  1.085  mills  ;   general  purposes, 
1.475  mills ;  new  capitol,  .6  mills  ;  canals,  .34  mills.    What  was  the 
total  rate  of  taxation,  and  how  much  was  raised  by  a  county  whose 
valuation  was  fixed  by  the  state  board  of  equalization  at  $11,047,534? 
How  much  was  raised  for  school  purposes? 

4.  The  state  tax  of  a  certain  county  was  $38,666.37,  and  the 
valuation  of  the  county,  $11,354,880.     How  much  of  this  tax  was 
paid  by  a  town  whose  valuation  was  fixed  by  the  board  of  super- 
visors at  $3,938,663.17? 

5.  The    total    county   expenses    of    the    same    county    were 
$25,063.35.     How  much  should  be  apportioned  to  the  above  town  ? 

6.  Taxes  were  levied  in  a  certain  town  for  the  following  pur- 
poses : — support  of  poor,  $2,000 ;  roads  and  bridges,  $500 ;  accounts 
audited  by  town  auditors,  $2,876.10 ;  accounts  audited  by  super- 
visors, $19.48 ;  county  expenses,  $9,774. 72  less  a  surplus  of  $6,055.90 
in  the  county  treasury ;  state  and  school  tax,  $15,079.88 ;    surplus 
tax,  $868.98.     What  was  the  rate  of  taxation,  the  total  valuation 
of  the  property,  as  made  by  the  town  assessors,  being  $4,321,252  ? 
What  was  the  tax  of  Mr.  A.,  whose  valuation  was  $7,300  ? 

7.  Find  from  the  following  table  the  tax  on  $16750. 

OPERATION.  ANALYSIS. — By  looking  in  the  table  oppo- 

Tax  on  $16000  is  $92.80     site  1  and  under  G,  we  find  that  the  tax  on 

<(  750   «        435      $16  is  $.0928,  and  by  removing  the  point  3 

IBT™  «    q^T^    places  to  tlie  right>  we  find  tlie  tax  on 

y'-lc      $16000  to  be  $92.80.     In  the  same  manner, 

the  tax  on  $750  is  found  to  be  $4.35.     The  tax  on  $16750  is  $92.80  plus 
$4.35,  or  $97.15. 

8.  How  much  was  paid  by  Mr.  B.  on  an  assessment  of  $6400, 
the  collector  charging  a  commission  of  \%  additional  ?    (Use  table.) 


TAXES. 


237 


NOTE. — To  save  labor  in  the  calculation  of  taxes,  a  table  similar  to  the 
following  is  usually  prepared  by  the  accountant. 

TAX  TABLE. — Kate,  5.8  mills  on  $1. 


0 

l 

2 

3 

4 

5 

6 

7 

8 

9 

1 

.0580 

.0638 

.0696 

.0754 

.0812 

.0870 

.0928 

.0986 

.1044 

.1102 

2 

.1160 

.1218 

.1276 

.1334 

.1392 

.1450 

.1508 

.1566 

.1624 

.1682 

3 

.1740 

.1798 

.1856 

.1914 

.1972 

.2030 

.2088 

.2146 

.2204 

.2262 

4 

.2.320 

.2378 

.2436 

.2494 

.2552 

.2610 

.2668 

.2726 

.2784 

.2842 

5 

.2900 

.2958 

.3016 

.3074 

.3132 

.3190 

.3248 

.3306 

.3364 

.3422 

6 

.3480 

.3538 

.3596 

.3654 

.3712 

.3770 

.3828 

.3886 

.3944 

.4002 

7 

.4060 

.4118 

.4176 

.4234 

.4292 

.4350 

.4408 

.4466 

.4524 

.4582 

8 

.4640 

.4698 

.4756 

.4814 

.4872 

.4930 

.4988 

.5046 

.5104 

.5162 

9 

.5220 

.5278 

.5336 

.5394 

.5452 

.5510 

.5568 

.5626 

.5684 

.5742 

9.  Mr.  D.  being  delinquent  was  charged  5%  additional.     How 
much  was  he  obliged  to  pay  on  a  valuation  of  $9500  ? 

10.  What  was  the  total  tax.  including  commission  of  1%  of 
Mr.  C.,  whose  real  estate  was  assessed  at  $24000,  and  personal 
property  at  $15500  ? 

11.  In  the  City  of  Brooklyn,  N.  Y.,  the  following  is  the  law 
regarding  the  payment  of  taxes  : 

On  all  taxes  and  assessments  which  shall  be  paid  to  the  collector,  before 
tbe  expiration  of  one  month  after  the  warrant  for  the  collection  of  the  same 
shall  have  been  delivered  to  him,  an  allowance  shall  be  made  at  the  rate  of 
7yV%  per  annum  for  the  unexpired  portion  thereof.  On  all  taxes  or  assess- 
ments paid  after  the  expiration  of  one  month  from  the  time  the  same  shall 
have  become  due  and  payable,  there  shall  be  added  to  such  tax  or  assessment 
interest  at  the  rate  of  9  %  per  annum. 

According  to  the  above  law,  how  much  tax  was  paid  Jan. 
16,  by  Mr.  A.,  the  valuation  of  whose  property  was  $7500,  the 
rate  of  tax  being  $2.376  per  $100,  and  the  warrant  having  been 
delivered  to  the  collector,  Jan.  4  ?  How  much  was  paid  by  Mr. 
B.,  on  a  valuation  of  $12500,  Mar.  26  ?  (365  days  to  the  year.) 

12.  What  is  the  total  tax  on  8375  pounds  tobacco  at  16&  4360 
gallons  distilled  spirits  at  70^,  2165  barrels  beer  at  $1  ? 

13.  How  much  is  the  semi-annual  tax   of  a  national  bank 
whose  average  circulation   is   $225,000  at  \%,  average  deposits 
$1,416,387  at  ±%,  average  capital  stock  $400,000  at  ±%  ? 


DUTIES. 


DEFINITIONS. 

488.  Duties  or  Customs  are  taxes  assessed  by  the  Govern- 
ment upon  imported  merchandise  for  the  purpose  of  revenue  for 
the  support  of  the  government  and  for  the  protection  of  home 
industry. 

1.  The  total  ordinary  revenues  of  the  United  States  for  the  fiscal  year 
ended  June  30,  1881,  were  $360,782,292,  of  which  $198,159,676  were  received 
from  customs.     Of  the  latter  amount,  $138,908,562  were  collected  at  the  port 
of  New  York,  leaving  $59,251,114  as  the  amount  collected  at  all  other  ports 
of  the  country. 

2.  The  waters  and  shores  of  the  United  States  are  divided  into  collec- 
tion districts  ;  in  each  of  which  there  is  a  port  of  entry  and  one  or  more  ports  of 
delivery.     Thus,  the  district  of  Boston  and  Charlestown  comprises  all  the 
waters  and  shores  within  the  counties  of  Middlesex,  Suffolk,  and  Norfolk. 
Boston   (including  Chelsea)  is  the  port   of  entry,  and   Medford,   Cohasset, 
Hingham,   Weymouth,  Cambridge,  Roxbury,   and  Dorchester,  the  ports  of 
delivery.     All  ports  of  entry  are  also  ports  of  delivery. 

3.  All  cargoes  chargeable  with  duties  shall  be  entered  and  the  duties 
paid,  or  secured  to  be  paid,  at  the  port  of  entry,  before  permission  shall  be 
given  to  discharge  the  same  at  the  port  of  delivery. 

4.  The  principal  officer  of  every  district  is  the  collector,  who  is  assisted 
by  deputy-collectors,  surveyors,  appraisers,  weighers,  gaugers,  inspectors,  etc. 
The  duties  of  the  above  vary  in  the  several  collection  districts  and  ports. 
There  is  also  in  the  leading  ports  of  entry,  a  "  naval  officer,"  whose  depart- 
ment is  a  check  upon  that  of  the  collector.     He  receives  copies  of  all  invoices 
and  entries,  estimates  duties,  countersigns  permits,  clearances,   certificates, 
debentures,  and  other  documents,  granted  by  the  collector. 

5.  The  surveyor  usually  superintends  and  directs  the  inspectors,  weigh- 
ers, and  gaugers,  within  his  port. 

6.  An  importer  desiring  a  permit  to  land  merchandise,  presents   his 
invoice,  with  the  consular  certificate,  bill  of  lading,  and  the  formal  entry 
attached  (See  Ex.  25,  Art.  499),  to  the  entry  clerk  at  the  custom-house,  and 
makes  the  necessary  oath  before  the  collector  or  his  deputy.     The  duties,  if 


DEFINITIONS.  239 

any,  are  estimated  in  the  departments  of  the  collector  and  the  naval  officer. 
The  amount  of  the  estimated  duties  having  been  paid,  or  secured  by  a  bond, 
the  collector,  together  with  the  naval  officer,  where  there  is  one,  grants  a  per- 
mit to  land  the  merchandise.  It  is  the  custom  of  custom-house  brokers  and 
many  merchants  to  calculate  the  duties  and  enter  the  same  on  the  entry. 

The  permit  is  presented  to  the  inspector  in  charge  of  the  vessel,  who 
allows  the  merchandise  to  be  landed.  The  collector  indicates  on  the  permit 
by  numbers  what  packages  shall  be  sent  to  the  public  store  for  exam- 
ination. 

When  the  merchandise  is  examined  by  the  appraiser  (495),  he  enters  on 
the  invoice  (494)  or  manifest  the  rate  of  duty  to  be  collected.  The  invoice 
and  the  accompanying  papers  are  then  sent  to  liquidators  in  both  the  collec- 
tor's and  naval  officer's  departments  for  adjustment.  The  liquidators  check 
the  calculations  on  the  entry,  or  again  calculate  the  duty  it'  the  appraiser  has 
changed  the  rate  or  the  dutiable  value,  or  if  the  returns  of  the  weigher  or 
gauger  differ  from  the  weight  or  measurement  in  the  invoice.  The  amount  of 
duty  to  be  refunded  or  collected  is  marked  on  the  entry,  if  the  difference 
between  the  duty  as  estimated  and  as  liquidated  is  less  than  $1,  it  is  disre- 
garded, and  the  liquidator  approves  the  original  estimate. 

489.  A  Custom-House  Broker  is  a  person  who  makes  entries, 
secures  permits,  and  transacts  other  business  at  custom-houses  for 
merchants.     He  is  familiar  with  the  tariff  laws  and  the  details 
and  regulations  of  custom-house  business,  and  usually  acts  under 
a  power  of  attorney. 

1.  The  necessary  blanks  for  making  entries  are  provided  by  the  broker, 
or  they  may  be  obtained  at  any  stationer's. 

2.  The  greater  part  of  the  business  at  the  New  York  custom  house  is 
done  through  brokers. 

490.  The  following  are  the  principal  entries  made  at  custom- 
houses : 

1.  Import  entry  of  merchandise  for  immediate  consumption. 

2.  Import  entry  of   merchandise  for  storage  in  a    bonded    warehouse, 
called  a  "  Warehouse  entry."     (See  Art.  49(5.) 

3.  Import  entry  of  merchandise  for  immediate  transportation  in  bond  (in 
sealed  cars)  to  another  port  of  entry  ;   as  goods  landed  at  New  York  to  be 
transported  in  bond  to  Chicago.     In  this  case  the  goods  are  appraised,  and 
the  duties  assessed  and  collected  at  Chicago. 

*  4.  Entry  of  merchandise  for  immediate  transportation  in  bond  to 
Canada  or  Mexico,  or  other  foreign  country.  In  this  case  no  duties  are 
collected. 

5.  Withdrawal  entry  from  bonded  warehouse  for  consumption   at  the 
place  of  importation.     (See  Art.  496.) 


240  DUTIES. 

6.  Withdrawal  entry  from  bonded  warehouse  for  immediate  transporta- 
tion in  bond  to  another  port  of  entry. 

7.  Withdrawal  entry  from  bonded  warehouse  for  immediate  transporta- 
tion in  bond  to  Canada,  Mexico,  or  other  foreign  country. 

8.  Export  entry  of  merchandise  manufactured  in  the  United  States,  for 
the  benefit  of  drawback  (497). 

491.  Duties  are  of  two  kinds,  ad  valorem  and  specific. 

492.  An  Ad  valorem  Duty  is  a  tax  assessed  at  a  certain 
per  cent  on  the  dutiable  value  of  the  merchandise ;  as  silks  at 

?,  watches  at  2-5$,  linens  30,  35  and  40%,  china  45  and  50%. 


1.  The  dutiable  value  ot  merchandise  is  its  market  value  at  the  port  cj! 
export,  but  not  less  than   its  invoiced  cost,  commission  added,  whether  paid 
or  not.     It  is  usually  the  original  cost  plus  all  charges,  excepting  the  consul's 
fee,  to  the  vessel  on  which  the  shipment  is  made.     The  charges  include  the 
transportation  to  the  place  of  export,  the  value  of  the  sack,  box,  etc.,  in 
which  the  merchandise  is  contained,  commission  at  the  usual  rates,  but  in  no 
case  less  than  %\%t  brokerage  and  all  other  charges,  except  the  consul's  fee. 
There  is  no  duty  on  the  freight  or  transportation  from  the  port  of  export. 
The  appraised  value  is  sometimes  greater  than  the  invoice  value  (494). 

2.  In  reducing  foreign  money  to  U.  S.  money  for  the  purpose  of  calcu- 
lating duties,  if  the  cents  of  the  result  are  less  than  50,  they  are  rejected  ;  if 
more  than  50,  $1  is  added  to  the  dollars. 

493.  A  Specific  Duty  is  a  tax  assessed  at  a  certain  sum  per 
ton,  pound,  foot,  yard,  gallon,  or  other  weight  or  measure,  with- 
out reference  to  the  value  ;  as  leaf  tobacco  at  35^  per  pound,  ale 
and  beer  (not  bottled)  20^  per  gallon,  clay  $5  per  ton,  plate  glass 
per  square  foot,  playing  cards  25  and  35  cts.  per  pack,  brandy  $2 
per  proof  gallon,  lumber  per  M  feet  board  measure,  salt  (in  bulk) 
8  cts.  per  100  Ibs.,  flaxseed  20  cts.  per  bushel  (56  Ibs.),  cotton 
goods  per  square  yard. 

1.  Before  specific  duties  are  calculated,  allowances  are  made    for  tare 
(the  weight  of  the  box,  barrel,  or  cask),  leakage  (of  liquids  in  barrels),  and 
breakage  (of  liquids  in  bottles,  usually  5  %\ 

2.  The  U.  S.  Custom  House  ton  contains  2240  Ibs.  (172,  3),  the  hundred- 
weight 112  Ibs.,  and  the  quarter  28  Ibs. 

3.  On  certain  goods,  there  is  both  a  specific  and  an  ad  valorem  duty 
(sometimes  called  a  combined  duty) ;  as  iron  wire  $20  3|  cts.  per  pound  and 
15%,  tobacco  pipes   (excepting  common  clay)   $1.50  per  gross  and   75  %, 
statuary  marble  $1  per  cubic  foot  and  25  % ,  woollen  goods  50  cts.  per  pound 
and  35^. 


DEFINITIONS.  241 

494.  An  Invoice  (277)  is  a  statement  made  by  the  seller  or 
shipper  of  merchandise  giving  a  description  of  the  same,  and  show- 
ing marks,  numbers,  quantity,  value,  charges,  and  other  details. 
(See  Ex.  26,  Art.  499.) 

1.  All  invoices  shall  be  made  out  in  the  weights  and  measures  of  the 
country  from  which  the  importation  is  made. 

2.  All  invoices  of  merchandise  subject  to  a  duty  ad  valorem,  shall  be 
made  out  in  the  currency  of  the  country  or  place  from  whence  the  importa- 
tion is  made. 

8.  When  the  value  of  the  foreign  currency  is  fixed  by  law  (see  Art. 
192),  the  value  is  to  be  taken  in  estimating  the  duties  ;  when  the  value  is 
not  fixed  by  law,  the  invoice  must  be  accompanied  by  a  consular  certificate 
showing  its  value. 

4.  All  invoices  of  importations  must,  before  the  shipment  of  the  mer- 
chandise, be  produced  to  and  authenticated   by  the  U.  S.  consular  officer, 
where  there  is  such  an  officer.     In  countries  without  a  U.  S.  consular  officer, 
the  authentication  is  made  by  a  consul  of  a  country  in  amity  with  the  United 
States  ;    or,  if  there  be  no  such  consul,  then  by  two  respectable  resident 
merchants. 

All  invoices  must  be  made  in  triplicate  ;  the  three  copies  to  be  regarded 
as  one  invoice,  and  subject  to  only  one  charge  for  consular  certificate.  One 
of  the  triplicate  invoices  is  returned  to  the  person  producing  them  ;  another 
is  carefully  preserved  in  the  office  of  the  consul ;  and  the  third  is  transmitted 
to  the  collector  of  the  port  of  destination  of  the  merchandise. 

5.  When  the  value  of  merchandise  imported  into  the  United  States  shall 
not  exceed  $100,  the  collector  is  authorized  to  admit  the  same  to  entry,  with- 
out the  triplicate  invoice  required  in  other  cases. 

495.  Aii  Appraiser  is  an  officer  of  the  customs  who  ex- 
amines imported  merchandise  and  determines  the  dutiable  value 
and  the  rate  of  duty  of  the  same. 

1.  The  place  where  the  examinations  are  usually  made  is  called  the 
"Public  Store." 

2.  One  package  of  every  invoice,  and  one  package  at  least  out  of  every 
ten   similar   packages,  shall    be   sent  to  the  public  store  for  examination. 
Certain  bulky  and  heavy  articles  are  examined  at  the  wharf  where  unloaded. 
Weighable  and  gaugable  goods  on  which  the  duties  are  specific,  are  not  sent  to 
the  public  store  for  examination. 

3.  Wrhen   the   appraised   value   of  any   merchandise   subject  to  an   ad 
valorem  duty  is  10%  more  than  the  invoice  value  as  entered  by  the  importer, 
then  in  addition  to  the  duty  imposed  by  law  on  the  same,  there  shall  be  col- 
lected 20  %  of  the  duty  imposed  on  the  same. 

496.  A  Bonded  "Warehouse  is  a  place  for  the  storage  of 
merchandise  on  which  the  duties  or  taxes  have  not  been  paid. 


242  DUTIES. 

1.  If  an  importer  does  not  desire  to  place  his  goods  at  once  in  the  mar- 
ket, or  anticipates  exporting  the  same,  by  giving  a  bond  for  the  payment  of 
the  duties  and  making  the  entry  in  the  proper  form,  he  may  have  the  mer- 
chandise stored  at  his  own  risk  in  a  bonded  warehouse,  and  thus  defer  the 
payment  of  the  duties. 

2.  The  importer  may  select  any  U.  S.  bonded  warehouse  in  which  to 
deposit  his  merchandise. 

3.  Merchandise  may  be  withdrawn  from  a  bonded  warehouse  for  expor- 
tation to  Canada  or  other  foreign  country,  without  the  payment  of  the  duty 
on  the  same. 

4.  Merchandise  is  frequently  sold  "in  bond"  at  prices  which  do  not  in- 
clude the  duty. 

5.  Merchandise  that  may  be  in  warehouse  under  bond  for  more  than 
one  year,  will  be  liable  when  withdrawn  for  10  ^  additional  duty. 

6.  Any  goods  remaining  in  public  store  or  bonded  warehouse  beyond 
three  years  shall  be  regarded  as  abandoned  to  the  government,  and  sold 
under  certain  regulations  and  the  proceeds  paid  into  the  Treasury. 

497.  Drawback.— When  distilled  spirits,  fermented  liquors, 
medicines,  and  perfumery,  upon  which  an  internal  revenue  tax 
has  been  paid,  and  foreign  merchandise  upon  which  an  import 
duty  has  heen  paid,  are  exported,  the  tax  or  duty  upon  the  same 
is  refunded.      Such    return    of    the    tax    or    duty    is   called   a 
Drawback. 

498.  The  Free  List  is  a  list  of  articles  which  are  exempt 
from  duty. 

In  making  entries  of  free  goods,  the  value  as  given  in  foreign  money 
must  be  reduced  to  U.  S.  money  (See  Ex.  28,  Art.  499),  permits  must  be 
obtained  to  land  the  goods,  and  certain  packages  are  sent  to  the  public  store 
for  examination. 

EXAMPLES. 

499.  1.  A  merchant  imported  from  Lyons  an   invoice  of 
silk,   the  dutiable  value  (492,   1)  of  which  was  4-8765  francs. 
What  was  the  dutiable  value  of  the  same  in  U.  S.  money,  and 
what  was  the  duty  at  60%  (4:92)  ? 

NOTES. — 1.  For  foreign  moneys  of  account  and  their  values  in  United 
States  money,  see  Art.  192. 

2.  48765  francs  at  19.3^  =  $****.  (See  Art.  486,  2.)  60^  of  $****  = 
$****.** 

2.  Find  the  duty  on  1617  pounds  of  almonds,  at  6  cts.  per 
pound. 


DUTIES.  243 

3.  What  were   the   average  daily  receipts  of  the  New  York 
custom-house  for  the  fiscal  year  ended  June  30,  1881,  making 
allowance  for  62  Sundays  and  7  holidays.     (See  Art.  488,  1.) 

4.  An  invoice  of  woollen  cloth  weighing   516  pounds,   and 
valued  afc  £327  16s,  was  imported  from  England.     What  was  the 
duty  at  50  cts.  per  pound  and  35$  ? 

5.  An  importer  on  making  his  entry  at  the  custom-house, 
paid  the  duty  on  38716  pounds  (Invoice  weight)  of  tobacco,  at 
35  cts.  per  pound.     According  to  the  return  of  the  custom-house 
weigher,  the  net  weight  was  38472  pounds.     How  much  of  the 
duty  was  refunded  when  the  entry  was  liquidated  ? 

6.  The  duty  on  28432  pounds  of  sugar  was  paid  at  the  rate  of 
2}  cts.  per  pound.    According  to  the  weigher's  return,  the  net 
weight  was   28218   pounds.      How   much   additional    duty   was 
collected,  the  appraiser  having  fixed  the   duty  at  3J  cts.   per 
pound  ? 

7.  Find  the  duty  on  an  invoice  of  linens  from  Ireland,  dutia- 
ble value  £424  15s.  6d.,  at  35%  ? 

8.  What  is  the  duty  on  an  invoice  of  porcelain  vases  from 
Paris  at  50%,  dutiable  value  9843  francs  ? 

9.  Find  the  duty  on  475  cu.  ft.  of  statuary  marble  imported 
from   Italy,    dutiable  value   16425  lire,    at   $1   per  cubic  foot, 

and  25%. 

10.  What  is  the  duty  on  37420  pounds  of  pig  iron  at  $7  per 
ton  (493,  2)  ? 

11.  Find  the  duty  on  an  invoice  of  leather  goods  from  Vienna, 
dutiable  value  6429  florins,  at  35%. 

12.  What  is  the  duty  on  an  importation  of  toys  from  Germany, 
dutiable  value  8437  marks,  at  50%  ? 

13.  What  is  the  duty  at  28  cents  per  sq.  yd.  and  35%,  on 
1248  yards  of  Brussels  carpet,  27  in.  wide,  invoiced  at  3s.  6d.  per 
yard,  shipping  charges  (less  consul's  fee)  £2  16s.  9d.  9 

14.  Find  the  duty  on  an  importation  from  Canada  of  5284 
bushels  of  potatoes,  invoiced  at  45  cts.  per  bushel,  and  37475 
pounds  of  hay,  invoiced  at  $1250  per  ton  (2000  Ibs.),  the  duty  on 
potatoes  being  15  cts.  per  bushel,  and  on  hay  20%. 


24:4: 


DUTIES. 


15.  On  a  certain  invoice  of  34216  pounds  of  pepper,  there  are 
discounts  for  damage  as  follows:   12$  on  6190  pounds,  8$  on 
6438  pounds,  and  5%  on  9642  pounds.     After  deducting  the  dis- 
count, what  would  he  the  duty  on  the  remainder  at  5  cents  per 
pound  ? 

16.  The  duty  on  burlaps  is  30$  ad  valorem.      What  is  the 
amount   chargeable   on   a   bale  containing  50   webs,   each  being 
54  yds.  and  16  in.  long,  and  27  in.  wide,  and  valued  at  30  cents  per 
sq.  yd.? 

17.  What  is  the  amount  of  duty  chargeable  on  2465  pounds  of 
wool,  valued  at  £171  8s.,  when  the  rate  of  duty  is  10  cts.  per  pound 
and  11$  ad  valorem? 

18.  The  duty  on  certain  glass  plates  being  35  cents  per  sq.ft., 
find  the  duty  on  316  boxes,  each  containing  20  plates,  and  each 
plate  being  24  in.  by  30  in. 

19.  Find  the  duty  at  25$,  on  one  engraving,  cost  in  London 
£34  5s.,  case  and  shipping  charges  15s.,  commission  2J$. 

20.  What  is  the  duty  at  $1  per  cu.  ft.  and  25$,  on  a  block  of 
marble   2x3x7/2.,  imported  from   Italy,    dutiable  value  3450 
lire? 

21.  Find  the  duty  on  4175  Ibs.  cloves  at  50.  per  lb.,  476  Ibs. 
cinnamon  at  20^,  and  5437  Ibs.  rice  at  2 


Make  the  extensions,  find  the  dutiable  value,  and  calculate  the 
duty  on  the  following  invoices  and  accompanying  entries: 

22.  Entry  of  merchandise,  imported  by  TEFFT,  WELLER  &  Co., 
from  Berlin  in  the  Str.  "Silesia."  Arrived  Jan.  14,  1882.  New 
York,  Jan.  16,  1882. 


Marks. 

Nos. 

Packages  and  Contents. 

605?. 

^ 

351 

One  case  half  silk  goods,    .     .     . 
Commission  2J$,       .     .     . 

Em.  ****.**©  23.8^      = 
60$  of  ****                    =      $***. 

Rm.  2399.80 

##*#  ** 

1***^** 

D  UTIES. 


245 


NOTE. — The  following  is  an  entry  of  free  goods.  Free  goods  are  entered 
and  the  foreign  monetary  units  reduced  to  U.  S.  money  for  statistical  purposes 
in  the  same  manner  as  dutiable  goods. 

23.  Entry  for  consumption  of  merchandise,  imported  by  W.  H. 
SCHIEFFELIX  &  Co.,  in  the  Str.  "Ailsa"  from  Savanilla,  on  the 
10th  day  of  January,  1882.  New  York,  Jan.  12,  1882. 


Free. 


33  bales  Medicinal  Bark, 2310. 

Packing, 12. 

Commission  2^,  **  ** 

(Pesos  of  U.  S.  of  Columbia),  .     .        ****  ** 

'$****. 

24.  Invoice  of  one  package  merchandise,  purchased  by  GLAD- 
HILL  &  Co.  for  account  of  D.  BUCKLEY  &  Co.,  New  York,  and 
forwarded  for  shipment  to  D.  &  C.  MAC!VER,  Liverpool. 

£.     s.     a. 

D.  B.    4  Pieces  Drab  Cotton  Pantaloon  32  in.  wide,  . 
207       #1729     79^, 

30  80, 

31  77$, 

32  79,   315$  (less  ^)  307  @  2s.  2d.,     .          **     *     * 

\\%  discount, 

Verification  and  Commissioner's  fee,      .  14   10 

2$%  Commission, 16     5 

**     * 

Less  Consul's  Certificate  (not  dutiable),  14   10 

33    11     7 

Entry  of  merchandise,  imported  by  D.  BUCKLEY  &  Co.  in  the 
Str.  "Catalonia"  from  Liverpool.  New  York,  Jan.  12,  1882. 

D.  B.          One  case  cotton, 33-11-7 

207  @  4.8665  ***** 

Duty  35^  of  $***  =          $**.** 


246 


D  UTIES. 


25.  Invoice  of  700  bales  leaf  cobacco  shipped  by  F.  B.  DEL  Rio 
&  Co.,  per  Sir.  "Niagara"  for  New  York,  and  consigned  to 
FREDERICK  DE  BABY  &  Co. 


F.  B.          700  bales  83077  Ibs.  (See  Art.  259,  Spain) 

CHARGES. 

3328/4027  Baling,        .......    $525. 

Export  duties,      .....    3407.39 

Consul  fee,       ......          2.75 

Small  charges,      .....     '49 


Commission 
Spanish  gold 
HAVANA,  Dec.  27,  1881. 


$35000 


**** 


I***** 


** 

** 


Custom  House,  New  York,  Collector's  Office,  Jan.  4,  1882. 
Bond  No.  9817. 

Entry  of  merchandise,  imported  on  the  third  day  of  January, 
1882,  by  FREDERICK  DE  BARY  &  Co.,  in  the  Str.  "Niagara" 
from  Havana. 


Marks. 

Nos. 

Packages  and  Contents. 

35c. 

F  B 

3338 

700  bales  Leaf  Tobacco 

84240  Ibs. 

$39958.74 

¥027 

@  .93,2= 

Duty  84240  Ibs.  @  350                   =  $*****. 
f  Weighers  return  83675  Ibs.  at  350  =    *****.** 

!«##**, 

Eefund,       ....         $***  .** 

t  Added  by  the  liquidator. 

26.  What  is  the  duty  on  an  invoice  of  crockery  invoiced  at 
£1275  16s.  6d.  /.  o.  1).  (free  on  board),  at  40%  ? 

27.  What  is  the  duty  on  28916  pounds  of  steel  rails  at  1J#  per 
pound,  and  11438  pounds  of  tin  plates  at  1TV^  per  pound? 

28.  The  duty  on  spool  thread  of  cotton,  containing  100  yds.  to 
the  spool,  is  6^  per  dozen  spools  and  in  addition  thereto  30%  ad 
valorem.     What  is  the  duty  on  11160  spools  valued  at  3^  a  spool? 


D UTIE  S. 


247 


29.  SHEFFIELD,  ENGLAND,  Dec.  14,  1881. 

Mr.  A.  R.  WHITNEY. 

Bought  of  THOS.  WIDDOWSON  &  Co. 


-/r 

c. 

gr. 

Ibs. 

I 

«. 

d. 

<^W\J1 

1  Cask  Corset  Steel  3|  x%6,  .  . 

12 

¥ 

21 

NX  JP 

1      "        "         "         " 

12 

0 

22 

83 

i         a            «              «              C*          . 

13 

0 

20 

#4 

1             (i                 f('               i(                  t( 

12 

2 

7 

** 

T 

** 

25/_ 

** 

** 

** 

4  Casks  6/-  each, 

* 

Carriage  to  Liverpool  1  6/ 

8   P 

er 

ton 

j    . 

* 

* 

* 

Shipping  Expenses      8/6 

" 

" 

. 

* 

* 

Consul's  Fee,    .... 

10 

4 

Commissioner's  Fee,  . 

4 

6 

W 

Entry  of  Merchandise,  imported  by  A.  R.  WHITNEY  in  the  Str. 
Gallia"  from  Liverpool.    New  York,  Dec.  30,  1881. 


t 

Four  Casks  Steel, 
Less  C.  C., 

Charges,    . 
****lbs.  @%y= 

*i 

£67  15s.  6d. 
14  10 

50  C.  3  qr.  14  Ib. 

@  4.8665    = 
1***^** 

67     0    8 
1  13     6 

68  14    2 

$*** 

NOTE.— On  all  merchandise  the  growth  or  produce  of  the  countries  east 
of  the  Cape  of  Good  Hope  (except  wool,  raw  cotton,  and  raw  silk,  as  reeled 
from  the  cocoon,  or  not  further  advanced  than  tram,  thrown,  or  organzine), 
when  imported  from  countries  west  of  the  Cape  of  Good  Hope,  there  is  levied 
a  discriminating  duty  of  10 %  ad  valorem  in  addition  to  the  duties  imposed  on 
any  such  articles  when  imported  directly  from  the  place  of  their  growth  or  pro- 
duction (R.  S.  2501).  If  the  following  goods,  which  are  on  the  "  Free  List " 
(41)8),  had  been  imported  directly  from  the  place  of  their  production,  there 
would  have  been  no  duty  on  the  same. 


248 


D  UTIE S. 


SO.  Invoice  of  fifty-six  (56)  packages  merchandise  (purchased 
in  London),  shipped  by  THOMAS  ROBINSON  per  Str.  "  City  of 
Lincoln,"  for  account  and  risk  of  and  consigned  to  McKESSON  & 
ROBBIES,  New  York. 


A  H  &  C 

GUM  A.NIMI 

£. 

s. 

4f  20  / 
»        /25 

C.    qr.     Ib. 

6  cases    8    2    23  net  @  £11  10s.,      .     . 
Discount  2J$,  

*** 
* 

* 
** 

Expense,      

#* 

** 
1 

M.  &R. 

COIR  FIBER. 

** 

** 

IVi't 

(?.     ?r.    0. 

50  bales    89    0    9  net  @  31s.  6d.     .     . 

*** 

* 

Brokerage,       

#** 
1 

** 

4 

CHARGES. 

*** 

* 

£.    «.     rf. 

Shipping  charges,  cartage,  etc.,  3  18     7 
Consul's  certificate,      .     .     .     .      14  10 

* 

** 

LONDON,  Dec.  21,  1881. 

*** 

** 

PORT  OF  NEW  YORK,  Jan.  6, 1882. 

Entry  for  Consumption  of  Merchandise,  imported  by  MoKES- 
&  BOBBINS  in  the  Str.  "  City  of  Lincoln,"  from  London  on 
the  fourth  day  of  January,  1 882. 


Marks. 


Numbers, 


Packages  and  Contertts. 


We. 


A.  H.  &  C. 


M.&R. 


Six  cases  Gum  Animi  (Gum  Copal). 

C.  qr,  Ib. 
wff.    8    2    23    975  Ib.  Cost,     . 


l/50 


Fifty  bales  Coir  Fiber. 

C.  or.  Ib. 
wg.    8U    0    9    9977^6.  Cost, 

Charges  (less  C.  C.), 


£***  *s.  *d.  @  4.86G5  =  $**»*. 

Discriminating  duty,  10^  of  $****  =     ***.  ** 


97.13.8 


141.10 
3.18.7 


PARTNERSHIP. 


DEFINITIONS. 

500.  Partnership  is  the  association  of  two  or  more  persons 
who  join  their  capital  and  services  for  the  purpose  of  conducting 
business,  the  gains  or  losses  being  shared  in  such. proportion  as 
may  be  stipulated  in  the  agreement. 

The  business  association  is  called  a  Firm,  House,  or  Company  ;  and  each 
individual  of  the  association  is  called  a  Partner. 

501.  A  Special  Partner  is  one  who  takes  no  active  part  in 
the  business,  and  whose  liability  is  limited  to  the  amount  of  his 
investment.     In  order  to  thus  limit  his  liability,  the  amount  of 
his  investment  must  be  duly  advertised,  and  he  must  take  no 
active  part  in  the  business. 

The  partners  who  conduct  the  business  are  called  General 
Partners.  Their  private  property  is  liable  for  the  debts  of  the 
partnership. 

502.  The  Capital  or  Capital  Stock  is  the  money  or  other 
property  which  is  invested  in  a  business. 

The  partners'  accounts  are  used  to  show  the  amounts  invested. 

In  most  firms,  the  investments  are  entered  in  the  partners'  "  stock  ac- 
counts," and  the  amounts  withdrawn  by  the  partners  during  the  year  and 
their  salaries  are  entered  in  their  "  private  accounts." 

503.  A  Resource  or  Asset  is  any  kind  of  property  belong- 
ing to  the  concern  having  a  financial  value. 

504.  A  Liability  is  a  debt  owing  by  the  concern. 

505.  The  Net  Worth  of  a  concern  is  the  excess  of  its 
resources  over  its  outside  liabilities. 


250  PARTNERSHIP. 

506.  The  Net  Insolvency  of  a  concern  is  the  excess  of  its 
outside  liabilities  over  its  resources.     The  concern  being  unable  to 
pay  its  debts  in  full,  it  is  said  to  be  insolvent. 

507.  G-ains  or  Losses,  how  shared. — In  most  partner- 
ships, the  gains  or  the  losses  are  divided  according  to  certain 
fractions  or  percentages  ;  the  inequalities  of  the  investments  are 
adjusted   by  allowing   interest   upon   the   same;    and    the   part- 
ners receive  salaries  for  their  services  rendered.      (See  Ex.  34, 
Art.   51O.)      Sometimes  the   net  gain  or  net  loss  is  shared  in 
proportion   to    the    investments    (Ex.    15,    Art.   51O),    or    the 
average   investments.      (Ex.    21,   Art.    51O.)      In    joint   stock 
companies  the  gains  (dividends)  and  the  losses  (assessments)  are 
shared  in  proportion  to  the  investment  or  the  amount  of  stock 
held. 

508.  G-ains  or  Losses,   how  found.— When  the  books 
have  been  kept  by  "Single  entry,"  and  when  no  books  have  been 
kept,  the  gain  is  found  by  subtracting  the  net  worth  (5O5)  at 
commencing,  or  the  investment,  from  the  net  worth  at  closing ; 
and  the  loss,  vice  versa. 

When  the  books  have  been  kept  by  "  Double  entry,"  the  gain 
may  be  found  as  above,  or  by  subtracting  the  sum  of  the  separate 
losses  from  the  sum  of  the  separate  gains.  The  results  by  the 
two  methods  should  be  the  same  and  should  prove  each  other. 


EXERCISES. 
5O9.  In  the  following  exercises  find  the  gain  or  the  loss  : 

1.  Capital  at  commencing,  $5000  ;  capital  at  closing,  $3000. 

2.  Capital  at  commencing,  $5000  ;  capital  at  closing,  $8000. 
8.   Capital   at   commencing,    $5000  ;    insolvency    at   closing, 

$1000. 

4-  Capital   at   commencing,    $5000  ;    insolvency    at   closing, 
$7000. 

5.  Insolvency  at  commencing,    $5000  ;    capital    at    closing, 
$2000. 

6.  Insolvency  at   commencing,    $5000 ;    capital    at    closing, 
$6000. 


PARTNERSHIP.  251 

7.  Insolvency   at   commencing,   $5000  ;    insolvency  at  clos- 
ing, $4000. 

8.  Insolvency   at   commencing,   $5000  ;    insolvency  at  clos- 
ing, $9000. 

Find  the  capital  or  the  insolvency  at  closing : 

9.  Capital   at   commencing,   $5000  ;    gain  during  the  year, 
00. 

10.  Capital   at   commencing,   $5000  ;    gain  during  the  year, 
00. 

11.  Capital   at   commencing,   $5000  ;    loss   during  the  year, 
00. 

12.  Capital   at   commencing,   $5000  ;    loss   during  the  year, 
(00. 

13.  Insolvency  at  commencing,  $5000  ;  gain  during  the  year, 
»00. 

14.  Insolvency  at  commencing,  $5000  ;  gain  during  the  year, 
'00. 

15.  Insolvency  at  commencing,  $5000  ;  loss  during  the  year, 
'00. 

16.  Insolvency  at  commencing,  $5000  ;  loss  during  the  year, 
00. 

Find  the  capital  or  the  insolvency  at  commencing: 

17.  Capital  at  closing,  $5000  ;  gain  during  the  year,  $3000. 

18.  Capital  at  closing,  $5000  ;  gain  during  the  year,  $6000. 

19.  Capital  at  closing,  $5000  ;  loss  during  the  year,  $4000. 

20.  Capital  at  closing,  $5000  ;  loss  during  the  year,  $9000. 

21.  Insolvency  at  closing,  $5000  ;  gain  during  the  year,  $1000. 

22.  Insolvency  at  closing,  $5000  ;  gain  during  the  year,  $8000. 
28.  Insolvency  at  closing,  $5000  ;  loss  during  the  year,  $2000. 
24.  Insolvency  at  closing,  $5000  ;  loss  during  the  year,  $7000. 


$3000 

10 
$6000. 

11. 
$2000. 

12 
$8000 

13 
$1000 

u 

$7000 
15 

$4000 
16 

$9000 


EXAMPLES. 


51O.  1.  A  and  B  are  partners,  A  sharing  f  of  the  gain  or 
loss  and  B  £.  A  invests  $5000,  and  B  $2350.  At  the  end  of  the 
year  their  resources  and  liabilities  are  as  follows :  merchandise  on 
hand,  per  inventory,  $2000 ;  real  estate,  $7000 ;  cash,  on  hand  and 


252  PARTNERSHIP. 

in  bank,  $1532 ;  due  on  personal  accounts,  81640.25 ;  notes  on 
hand,  $1000;  notes  outstanding,  $800;  owing  by  the  concern  to 
sundry  persons,  $4471.69.  What  is  the  amount  of  net  resources 
belonging  to  each  partner  ? 

FIRST  OPERATION. 

RESOURCES. 

Merchandise  on  hand,  .        .        $2000 
Real  estate,  ....          7000 
Cash  on  hand,       .        .        .          1532 
Personal  accounts,        .        .          1640.25 
Bills  receivable,    .        ...          1000  $13172.25 

LIABILITIES. 

Bills  payable,        .        .        .          $800 
Personal  accounts,        .        .          4471.69          5271.69 

Present  worth, $7900.56 

Investments  (subtracted),     ....      7350. 

Total  net  gain,         .        ,        .  $550.56 

f  of  $550.56  =  $367.04,  A's  share  of  the  gain, 
i  of  $550.56  =    183.52,  B's  share  of  the  gain. 

A's  investment,    .        .        .        $5000 
Plus  his  gain,        .        .        .  367.04 

Equals  his  present  worth,    ....     $5367.04 

B's  investment,     .        .        .        $2350. 

Plus  his  gain,       .        .        .  183.52 

Equals  his  present  worth,   ....     $2533.52 

Total  present  worth,  as  above,    .        .        .     $7900.56 

SECOND  OPERATION. 

ANALYSIS. — Theoretically,  all  the  resources  of  a  business  belong  to  the 
creditors  and  the  partners  (proprietors),  the  partners'  investments  being 
regarded  as  liabilities ;  hence,  the  resources  and  liabilities — including  the 
partners'  accounts — should  be  equal.  If  in  a  statement  of  the  condition  of  a 
business,  the  resources  and  liabilities  thus  considered  should  not  be  equal,  it 
is  evident  that  the  partners'  accounts  do  not  show  their  true  interests,  and 
the  inference  is  that  a  gain  or  loss  has  occurred  which  has  not  been  entered 
to  their  accounts.  The  excess  of  resources  over  liabilities  would  in  such 
case  show  the  gain,  as  would  the  excess  of  liabilities  over  resources  show  the 
loss.  In  order  to  restore  the  equilibrium,  the  gain  should  be  credited  or  the 
loss  debited  to  the  partners'  accounts. 


PARTNERSHIP 


253 


1.  STATEMENT  BEFORE  ADJUSTING  PARTNERS'  ACCOUNTS. 


RESOURCES. 


LIABILITIES. 


Merchandise, 
Real  estate, 
Cash,  . 

Personal  accounts, 
Bills  receivable,  . 


2000 

Bills  payable,    . 

7000 

Personal  accounts, 

1532 

A's  investment, 

1640.25 

B's         do. 

1000 

13172.25 

12621.69 

800 

4471.69 
5000 
2350 

12621.69 


Excess  of  resources  (net  gain),     550.56.    A's  f ,  $367.04  ;  B's  |,  $183.52. 


2.  STATEMENT  AFTER  ADJUSTING  PARTNERS'  ACCOUNTS. 


RESOURCES. 
Merchandise, 
Real  estate, 
Cash,   .        .    •     . 
Personal  accounts, 
Bills  receivable,  . 


2000 

7000 

1532 

1640.25 

1000 


13172.25 


LIABILITIES. 
Bills  payable,    . 
Personal  accounts,     . 
A's  investment  and  gain, . 
B's         do. 


800 

4471.69 
5367.04 
253352 

13172.25 


2.  A  and  B  are  partners,  A  sharing  f  of  the  gain  or  loss  and 
B  £.  A  invested  $5000,  and  B  $2350.  During  the  year  the  con- 
cern gained  on  merchandise,  $955.56 ;  on  real  estate,  $315.  The 
expense  account  showed  a  loss  of  $675 ;  the  interest  account,  $45. 
What  was  the  net  gain,  and  balance  of  each  partner's  account. 

NOTE. — The  above  example  is  the  complement  of  Ex.  1.  The  books 
having  been  kept  by  double  entry,  the  separate  gains  and  losses  are  given, 
and  the  net  gain  thus  found.  The  loss  and  gain  account  and  the  partners' 
accounts  are  shown  in  the  following  operation  in  "  skeleton  ledger  "  form. 


OPERATION. 


B. 


Balance, 

5367 

04 

Investment, 

2000 

Gain,    .    . 

367 

5367 

04 

5367 

Balance,   . 

5367 

Balance, 

2533 

52 

Investment, 

2350 

Gain,    .    . 

183 

53 

2533 

52 

2533 

52 

Balance,   . 

2533 

53 

Loss  AND  GAIN. 


Expense,  .    . 

675 

Mdse.,      .    . 

955 

56 

Interest,    .    . 

45 

Real  Estate, 

315 

A's  Gain  |,   . 

367 

04 

&*     ••     J,    . 

183 

52 

1270 

56 

1270 

56 

254  PARTNERSHIP. 

3.  A  and  B  started  in  business  July  1,  1881.     Each  put  into 
the  concern  $2200.     The  resources  on  Jan.  1,  1882,  were  as  fol- 
lows: goods,  $4000;  bills  receivable,  $1500.     The  liabilities  were 
$580.     A  has  drawn  out  cash,  $3000 ;  and  B,  $2000.     How  much 
is  due  each  partner,  the  gain  or  loss  being  divided  equally  ? 

NOTE. — It  must  be  "borne  in  mind  that  the  amounts  drawn  out  by  the  part- 
ners are  as  fully  resources  of  the  business  as  if  charged  to  an  outside  party. 

4.  On  Jan.  1,  my  brother  and  I  started  a  business  in  which  I 
invested  $900,  and  he  $400.     We  now  propose  to  separate,  and  the 
business  stands  as  follows :    stock  in  store,  $1800 ;  cash  on  hand 
and   in   bank,   $1200;    outstanding   accounts,   considered   good, 
$1200.     According  to  the  agreement,  I  am  entitled  to  -f  of  the 
net  gain,  and  my  brother  ^.     During  the  time  of  the  copartner- 
ship, I  have  drawn  $4000  and  he,  $2800.     Of  the  assets  given 
above,  how  much  are  we  each  entitled  to  ? 

5.  C,  D,  and  E  are  partners,  each  investing  $10000,  and  each 
to  share  J  of  the  gain  or  loss.     The  resources  and  liabilities  at 
the  close  of  business  are  found  to  be  as  follows,  viz. :  Merchandise 
on  hand,  per  inventory,  $8159.50;  cash  on  hand,  $5012.88  ;  per- 
sonal accounts  due  the  firm,  $4235  ;  notes  and  accepted  drafts 
(bills  receivable)  on  hand,  $5000  ;  real  estate,  $8000 ;  bonds  and 
stocks,   $12000  ;    owing   by  the  firm  to  sundry  persons,  $5505  ; 
firm's  notes  outstanding  (bills  payable),  $3000.     C  lias  withdrawn 
during  the  year  $1247.87 ;    D,  $1400 ;    and  E,  $1489.     What  is 
each  partner's  interest  in  the  concern  at  closing  ? 

6.  C,  D,  and  E  are  partners,  sharing  the  gains  and  losses 
equally.     C's  net  investment  was  $8752.13  ;  D's,  $8600 ;  and  E's 
$8511.     During  the  year  the  firm's  gains  were  as  follows:  Mer- 
chandise, $8529  ;  stocks  and  bonds,  $650  ;  interest,  $985.25.    The 
cost  of  conducting  the  business  was  $2125.     What  was  each  part- 
ner's interest  at  closing  ? 

7.  M  and  N  are  partners,  M  sharing  J  of  the  gain  or  loss  and 
N  £.     M  invested  $15000  and  N  $5000.     At  the  close  of  the  busi- 
ness year,  the  resources  and  liabilities  of  the  concern  are  as  fol- 
lows :  cash  on  hand,  $2128  ;  bills  payable,  $4000 ;  bills  receivable, 
$3000  ;  the  firm  owes  sundry  persons,  $8375  ;  due  the  firm  from 
sundry  persons,  $16427  ;  rent  paid  in  advance,  $375  ;   mortgage 
held  by  the  concern  on  the  property  of  A.  G.  Pope,  $5000 ;  accrued 


PARTNERSHIP.  255 

interest  on  the  same,  $150 ;  store  fixtures  valued  at  $835  ;  mer- 
chandise on  hand,  $9416 ;  accrued  interest  on  firm's  notes  out- 
standing, $112 ;  accrued  interest  on  notes  held  by  the  firm,  $75. 
M  has  withdrawn  $2465 ;  and  N,  $2275.  According  to  the  agree- 
ment, each  partner  is  to  receive  a  salary  of  $2500.  What  are  the 
separate  interests  at  the  close  of  the  business  ? 

8.  R,  S,  T,  and  U  enter  into  copartnership  with  equal  capital, 
upon  the  following  conditions  :    R  to  receive  as  a  salary  $2000  ; 
S,  $1500;    T,   $1200;   and   U,   $1000;   the   gain  or  loss   to   be 
divided  equally.     At  the  close  of  the  year,  the  net  gain,  exclusive 
of  salaries,  proves  to  be  $5400.     To  how  much  of  this  amount  is 
each  entitled  ? 

9.  X,  Y,  and  Z  commence  business  without  capital.     Accord- 
ing to  the  partnership  contract,  X  is  to  receive  a  salary  of  $3000 ; 
Y,  $2500  ;  and  Z,  $2000 ;  the  gain  or  loss  to  be  divided  equally. 
During  the  year,  X  withdraws  $3000  ;  Y,  $2800  ;  and  Z,  $1800. 
What  is  the  balance  clue  each  partner  at  the  end  of  the  year,  if 
the  gain,  without  taking  into  account  the  partners'  salaries,  is 
$9000  ? 

10.  A  and  B  are  partners,  A  investing  f  of  the  capital,  and 
B  ^ ;    the  gains  or  losses  to  be  shared  in  the  same  proportion. 
The  following  is  an  exhibit  of  the  business,  excepting  the  part- 
ners' accounts,  at  the  close  of  a  certain  period  :  Resources,  cash, 
$3775 ;   Stone  &  Co.,  $150 ;  A.  R.  Mead,  $1200  ;  bills  receivable, 
$5500  ;  interest  on  the  same,  $125  ;  merchandise,  $5140.     Liabil- 
ities, L.  Blair,  $500;    W.  H.  Rice,  $723;    Martens  &  Bultman, 
$517.64  ;   bills  payable,  $3300  ;  interest  on  the  same,  $169.     The 
net  gain  during  the  year  was  $3174.     What  was  each  partner's 
original  investment  ? 

11.  Upon  a  close  valuation  of  the  personal  accounts  due  the 
firm  in  the  preceding  example,  the  partners  are  convinced  that 
Stone   &    Co.'s   is   worth  no  more   than   50^    of  its   face ;    and 
A.  R.  Mead's,  25%  of  its  face.     Upon  this  valuation  what  would 
be  the  gain,  and  what  the  condition  of  the  partners'  accounts  at 
closing  ? 

12.  P  and  Q  are  partners,  each  to  receive  interest  on  his  net 
investment  at  the  rate  of  G%  per  annum,  and  the  net  gain  or  loss 
to  be  divided  equally.     P  invests,  Jan.  1,  $5000  ;  Mar.  1,  $4000 ; 
June  16,  $1500  ;  and  draws  out  Apr.  16,  $2500.     Q  invests,  Jan.  1, 


256  PARTNERSHIP. 

$8000  ;  Sept.  16,  $2000;  and  draws  out  June  1,  $1500  ;  Nov.  11, 
$500.  At  the  close  of  the  year,  the  net  gain  is  found  to  be 
$4475.25,  without  taking  into  account  the  interest  on  the  part- 
ners' accounts.  What  is  the  amount  due  each  partner  after  the 
gain  is  adjusted  ?  (Time  by  Compound  Subtraction.) 

13.  A  and  B  have  been  doing  business  as  partners,  A  sharing 
|  and  B  f  of  the  gains  and  losses.     A  invested  $4500,  average  date 
Mar.  25,  1882  ;  and  drew  out  $2700,  average  date  Sept.  12,  1882. 
B  invested  $7200,  average  date  June  17,  1882  ;    and  drew  out 
$3750,  average  date  Oct.  25,  1882.     At  the  time  of  their  dissolu- 
tion, Jan.  1,  1883,  the  debts  of  the  firm  were  all  paid  and  they 
had  on  hand  belonging  to  the  firm  $8750  in  cash.     How  shall 
the  money  be  divided,  each  being  allowed  interest  at  6^  on  his 
investment   and   charged   with   interest  at  the  same  rate  on  the 
amounts  drawn  ?     (Time  by  exact  days.     Interest  360  days  to  the 
year. ) 

14.  A  and  B  are  partners,  A  having  -|  and  B  f  interest.     A 
advanced  in  business  $12000,  average  date  Jan.  12,  1883  ;    and 
drew  out  $1265,  average  date  Oct.  20,  1883.     B  advanced  $7500, 
average  date  Apr.  5,   1883;    and   drew  out  $2560,  average  date 
Nov.  25,   1883.    Jan.  1,  1884,    A  purchases  B's  interest  in  the 
business,  and  at  that  date  the  assets  are  as  follows  :  Cash,  $5800  ; 
merchandise,  $6250  ;  notes  on  hand,  $7300;  accrued  interest  on 
the  same,  $387.14;  personal  accounts,  $5700.     The  liabilities  are 
as  follows  :    Notes  outstanding,  $4200  ;  accrued  interest  on  the 
same,    $227.65 ;    personal   accounts,   $2500.      How   much   is   B 
entitled  to,  5%  of  the  personal  accounts  being  considered  uncol- 
lectible, and  interest  being  reckoned  on  the  partners'  accounts  at 
6$  per  annum  (365  days  to  the  year)  ? 

15.  A  and  B  are  partners  in  business,  the  gain  or  loss  to  be 
divided  in  proportion  to  investment.     A  invested  $8750  ;  B  in- 
vested $4000.     The  net  gain  is  $2726.15.     What  is  each  partner's 
share  ? 

FIRST  OPERATION. — FRACTIONAL  METHOD. 

ANALYSIS. — Since  A's  investment,  $8750,  is  TVWV  of  tlie  total  investment, 
he  is  entitled  to  ^Wo  of  *^e  ga™  >  and  for  a  similar  reason,  B  is  entitled  to 

.|s  of  12720.15  =  $1870.89,  A's  ffain. 
H  of  $2726.15  =  $855.26,  B's  gain. 


PARTNERSHIP.  257 

SECOND  OPERATION.— BY  PROPORTION. 

ANALYSIS. — The  total  investment  is  to  each  partner's  investment  as  the 
total  gain  is  to  each  partner's  gain. 

$12750  :  $8750  ::  $2726.15  :  $1870.89,  A's  gain. 
$12750  :  $4000  ::  $2726.15  :    $855.26,  B's  gain. 

NOTE. — Cancel  any  factor  common  to  the  given  extreme  and  either  of 
the  means. 

THIRD  OPERATION. — BY  PERCENTAGE. 

ANALYSIS.— $2726.15,  the  gain,  is  21.3818$.  of  $12750,  the  total  invest- 
ment. The  partners'  gains  are  therefore  21.3816%  of  •  their  respective 
investments. 

21.3816^  of  $8750  =  $1870.89,  A's  gain. 

21.3816$  of  $4000  =    $855.26,  B's  gain. 

NOTE. — In  order  to  produce  exact  results  by  this  method,  it  is  necessary 
to  extend  the  number  expressing  the  rate  per  cent,  of  the  gain  or  loss  to 
several  decimal  places. 

16.  E,  F,  G,  and  H  enter  into  a  joint  speculation.    E  advances 
$5000,  F  $7000,  G  $8000,  and  H  $10000,  the  gain  or  loss  to  be 
divided  according  to  investment.     They  gain   $14285.     What  is 
.the  share  of  each  ? 

17.  Four  merchants  ship  goods  on  joint  account.     A  puts  in 
$6000,  B  $5500,  0  $4200,  and  D  $4800.     What  will  be  each  man's 
share,  if  the  gain  is  $9200  ? 

18.  A  lot,  whose  front  is  240  feet  and  whose  depth  is  100  feet, 
is  bought  by  A,  B,  and  0,  who  pay  respectively  $3000,  $4000,  and 
$5000.     How  many  feet  front  is  each  entitled  to,  if  it  is  divided 
in  proportion  to  their  investments  ? 

19.  Five  persons  having  claims  against  the  government,  placed 
their  claims  in  the  hands  of  an  agent  for  collection  ;  A's  claim 
amounted  to  $500,  B's  to  $425,  C's  to  $300,  D's  to  $250,  and  E's 
to  $175;  but,  after  the  agent  had  deducted  his  fees,   there  re- 
mained only  $1237.50.     How  much  did  each  claimant  receive  ? 

%0.  A  and  B  are  partners^.  They  have  cash  and  notes  on  hand 
to  the  amount  of  $6475.28.  A  has  drawn  from  the  concern  $2478.30, 
and  B  has  drawn  $1016.48.  A  invested  $4287.46,  and  B,  $1037.75. 
The  firm  owe  sundry  persons  $5016.82.  What  is  each  partner's 
present  interest  in  the  concern,  if  they  share  equally  in  gains  and 
losses  ? 


258 


PAR  TNE  RSHIP. 


21.  A  and  B  are  partners,  gain  or  loss  to  be  divided  in  pro- 
portion to  average  investment.  A  invests,  Jan.  1,  $4000 ; 
Mar.  1,  $2000  ;  Oct.  1,  $3000 ;  and  withdraws  July  1,  $1500  ; 
Dec.  1,  $1000.  B  invests,  Jan.  1,  $6000  ;  Sept.  1,  $3000.  They 
close  their  books  Jan.  1  of  the  following  year  and  find  they  have 
gained  $3456.  What  is  each  partner's  share  ? 

NOTE. — An  Average  Investment  is  an  investment  for  a  certain  period  of 
time  equivalent  to  several  investments  for  different  periods  of  time. 


OPERATION. 

A  invested    Jan.  1,        $4000  x  12  : 
Mar.  1,         2000  x  10 
Oct.  1,  3000  x     3  : 

A  withdrew  July  1,          1500  x     6 
Dec.  1,          1000  x     1  : 

A's  average  investment  for  1  month, 

OR, 

A  invested    Jan.  1, 
Mar.  1, 


2  = 


$4000 
2000 
6000  x     4  = 
withdrew  July  1          1500 

4500  x'   8  = 
invested    Oct.  1,          3000 

7500  x     2  = 
withdrew  Dec.  1,          1000 

6500  x    1  = 
A's  average  investment  for  1  month, 


$48000 
20000 

JMMM)   77000 
9000 

_i_qoo   10000 

67000 


$8000 
24000 
13500 
15000 

6500 
$67000 


ANALYSIS. — By  the  first  operation,  we  suppose  each  investment  to  be 
made  for  the  remainder  of  the  time.  To  find  the  average  investment,  multi- 
ply each  investment  and  withdrawal  by  the  interval  between  its  date  and 
>time  of  settlement.  Subtract  the  products  obtained  from  the  withdrawals 
from  the  products  obtained  from  the  investments.  The  remainder  will  be  the 
average  investment  for  1  month,  if  the  time  is  found  in  months.  A's  invest- 
ment of  Jan.  1  is  in  the  business  12  months  (Jan.  1  to  Jan.  1);  the  use  of 
$4000  for  12  months  is  equivalent  to  the  use  of  $"48000  for  1  month.  Treating 
the  other  investments  in  like  manner,  we  find  A's  total  investments  are 
equivalent  to  $77000  for  1  month.  A's  withdrawals  are  equivalent  to  $10000 
for  1  month.  A's  net  average  investment  is  therefore  equivalent  to  $67000 
for  1  month. 

By  tho  second  operation,  we  find  the  actual  amount  in  the  business  for 
each  month  of  the  year.  Jan.  1,  A  invested  $4000,  which  was  in  the  business 
until  Mar.  1,  or  for  2  months.  Mar.  1,  he  added  $2000,  making  his  total  invest- 


PARTNERSHIP.  259 

ment  $6000,  which  was  in  the  business  until  July  1,  or  for  4  months.  July  1,  he 
withdrew  $1500,  leaving  in  the  business  $4500  until  Oct.  1,  or  8  months,  etc. 
The  several  net  investments  as  found  in  this  manner  are  equivalent  to  $67000 
for  1  month. 

B's  average  investment,  as  found  by  either  of  the  above  methods,  is 
$84000  for  1  month. 

A's  average  investment  for  the  year  is  $5583.33*  ;  and  B's,  $7000.  To 
avoid  fractions,  divide  the  gain  in  proportion  to  the  average  investments  for 
1  month.  After  the  average  investments  are  found  for  a  common  time,  the 
gain  may  be  divided  according  to  either  of  the  methods  under  Ex.  15.  By 
the  fractional  method,  A  would  be  entitled  to  T6g7T  of  the.  gain,  and  B  to  T8g\. 

22.  0  and  D  are  partners,  gain  or  loss  to  be  divided  in  propor- 
tion to  average  investment.     C  puts  in  $6000  for  one  year,  and 
$7000  for  one  and  a  half  years ;  D  puts  in  $6000  for  two  and  a 
half  years.     The  net  loss  is  $1565.40.     What  is  each  one's  share  ? 

23.  A,  B,  and  C  are  partners.     A  puts  into  the  concern  $3000, 
but  withdraws  half  of  it  at  the  end  of  6  months  ;  B  puts  in  $2000, 
and  adds  $500  to  it  at  the  end  of  4  months ;  C  puts  in  $2500  for 
the  whole  year.     The  gain  during  the  year  is  $1700.     What  is 
each  one's  share  ? 

24.  Three  contractors  agree  to  build  a  road  for  $10000.    A  has 
25  men  at  work  for  16  days  and  30  men  for  34  days.     B  has  40 
men  for  10  days  and  45  men  for  40  days.     C  has  48  men  for  50 
days.     C  receives  $200  extra  for  superintending  the  work.     How 
much  is  each  contractor  entitled  to  ? 

25.  J,  K,  and  L  are  partners,  gain  or  loss  to  be  divided  accord- 
ing to  average  investment.     J  invests  as  follows  :  Jan.  1,  $6000  ; 
Apr.   1,  $4000 ;   K  invests,  Jan.    1,   $8000  ;   L  invests,   Jan.   1, 
$7000;  Apr.  16,  $2500  ;  and  draws  out  June  16,  $3500.     At  the 
end  of  the  year  the  net  gain  is  found  to  be  $4135.60.     What  is 
each  partner's  share  ?     (Time  by  Compound  Subtraction.) 

26.  A,  B,  C,  and  D  were  partners  for  two  years.     When  the 
firm  commenced  business,  A's  investment  was  $6000,  B's  $3500, 
C's  $2800,  and  D's  1700.     At  the  end  of  8  months,  A  withdrew 
$3000.     At  the  end  of  10  months,  D  added  $1300  to  his  former 
investment.     At  the  end  of  one  year,  B  withdrew  $800.     At  the 
close  of  the  two  years,  they  had  gained  $4727.     What  was  each 
partner's  share  of  the  gain  ? 

27.  A  and  B  are  partners  for  one  year,  the  gain  or  loss  being 
divided  in  proportion  to  their  average  investments.     A  invested, 
Jan.  1,  $8000 ;   June  16,  $1500  ;   Aug.  1,  $2500 ;    and  drew  out 


260  PARTNERSHIP. 

May  1,  $1500.  B  invested,  Jan.  1,  $10000;  Apr.  1,  $500;  and 
withdrew  Aug.  16,  $2500.  How  much  should  A  invest  Sept.  1  to 
entitle  him  to  one-half  the  gain  ? 

28.  A,  B,  and  C  form  a  copartnership  under  the  following  con- 
ditions :   A  is  to  manage  the  business,   and  to  receive  therefor 
$2400  per  annum,  which  amount  is  to  be  credited  as  July  1.     He 
is  to  receive  interest  on  his  salary  and  to  pay  interest  on  sums  with- 
drawn at  the  rate  of  Q%  per  annum.     B  and  0  are  to  furnish  the 
capital,  and  to  receive  interest   therefor  at  the  rate  of  6%  per 
annum.     The  net  gain  or  loss  to  be  divided  equally.     B  invests, 
Jan.  1,  $10000 ;  Apr.  1,  $5000.   C  invests,  Jan.  1,  $10000  ;  July  1, 
$5000  ;  and  draws  out  Sept.  16,  $500.     A  draws  out,  Feb.  1,  $200  ; 
Mar.   1,  $400;  July  11,  $500;  Oct.  1,  $200;  Nov.  21,  $100.     At 
the  end  of  the  year,  the  gain — without  taking  into  account  either 
the  salary  to  be  paid  to  A  or  the  interest  on  the  partners'  accounts — 
is  $8437.16.     What  will  be  the  balance  of  each  partner's  account, 
when  all  the  items  have  been  properly  entered  ? 

29.  C  and  D  are  partners.     According  to  agreement  C  is  to 
share  f  of  the  gain  or  loss,  and  D  J.     At  the  end  of  the  year,  D 
desires  to  increase  his  investment  so  that  he  will  be  entitled  to  a 
J-  interest.     How  much  must  D  invest,  the  partners'  accounts  after 
the  books  are  closed  being  as  follows  :     C's  debit,  $6712.38  ;  C's 
credit,  $27000  ;  D's  credit,  $9000  ? 

30.  A  and  B  buy  a  ship  for  $80000,  A  having  |  interest  and  B 
•f.     Subsequently  0  pays  $40000  for  -J  interest,  and  A  and  B  agree 
to  have  each  £  interest.     How  is  the  $40000,  which  C  pays  in, 
divided  between  A  and  B  ? 

31.  A,  B,  and  C  are  partners,  A  investing  $25000  capital,  B 
$5000,  and  C  nothing.     The  proportionate  interests  are  :  A  60%, 
B  25%,  C  15%.     At  the  expiration  of  the  term  of  copartnership, 
and  after  the  gains  and  losses  have  been  adjusted,  A's  credit  of 
capital  stands  intact,  B  has  a  credit  of  only  $1000,  while  C  has 
overdrawn  his  account  $8534.     C  being  insolvent,  howr  much  must 
B  pay  into  the  concern  to  adjust  his  share  of  the  loss  ? 

32.  M,  the  owner  of  a  mill,  employs  S,  a  miller,  under  the  fol- 
lowing conditions:  M  is  to  furnish  the  requisite  capital,  and  S  to 
receive,  in  lieu  of  salary,  -J  of  the  profits.     M  has  a  store  connected 
with  the  mill,  on  the  books  of  which  are  entered  all  time  sales  of 
mill  products.     The  grain,  etc.  for  the  mill  is  furnished  by  M. 
At  the  beginning  of  the  year  the  value  of  the  grain,  flour,  feed, 


PARTNERSHIP.  261 

etc.  is  $1727.  During  the  year  M's  purchases  for  the  mill  amount 
to  $19275.  S  has  received  for  cash  sales  $16337,  of  which  he  has 
paid  over  to  M  $15550.  The  sales  on  account,  as  shown  on  M's 
books,  amount  to  $8375 ;  and  the  value  of  the  products  on  hand  is 
$2828.  During  the  year  S  has  purchased  goods  at  M's  store  to  the 
amount  of  $837.65.  How  much  is  owing  to  S  at  the  expiration 
of  the  year? 

83.  A  and  B  form  a  copartnership  Jan,  1,  1878,  A  having  J 
interest  and  B  J.  For  the  purpose  of  a  valuation  to  be  covered 
by  insurance,  the  inventory  of  merchandise  is  increased  at  the  end 
of  the  first  year  $1550.  Jan.  1,  1879,  the  terms  of  copartnership 
are  changed,  A  having  \  interest  and  B  -|.  At  the  end  of  this 
year,  the  inventory  is  increased  fictitiously  $700  more,  or  $2250  in 
all.  The  same  basis  of  copartnership  continues  for  the  year  1880, 
at  the  close  of  which  year  the  inventory  is  additionally  increased 
$1293.75.  Jan.  1,  1881,  the  terms  of  copartnership  are  readjusted, 
A  having  T%,  and  B  T%-  interest.  At  the  close  of  this  year  the 
inventory  was  increased  additionally  $432.50.  Jan.  1,  1882,  the 
copartnership  was  made  equal,  each  partner  holding  a  half  interest. 
The  proposition  is  now  made  to  so  adjust  this  fictitious  valuation 
that  each  of  the  partners  shall  be  properly  credited  in  accordance 
with  the  new  terms  of  copartnership.  1.  What  entry  should  be 
made  to  accomplish  this  purpose  ?  2.  What  entry  should  be  made 
to  cancel  the  fictitious  valuation  of  merchandise,  and  place  the 
partners'  accounts  in  the  proper  condition  ? 

SJf.  A,  B,  and  C  are  partners,  A  sharing  f  of  the  gain  or  loss, 
B  f,  and  0  £.  Interest  is  to  be  reckoned  at  the  rate  of  6%  per 
annum  (365  days  to  the  year)  on  the  partners'  accounts,  and  each 
partner  is  to  receive  a  salary  of  $1800,  to  be  credited  as  July  1. 
A  invested,  Jan.  1,  $16000  ;  and  withdrew  during  the  year  $4875, 
average  date,  Aug.  21.  B  invested,  Jan.  1,  $20000  ;  and  with- 
drew $6224,  average  date,  June  18.  C  invested,  Jan.  1,  $5000  ;  and 
withdrew  $2625,  average  date,  July  31.  Jan.  1,  of  the  following 
year,  the  merchandise  account  shows  a  gain  of  $18437.16;  the 
interest  account  (not  including  the  interest  on  the  partners' 
accounts)  a  gain  of  $586.38  ;  sundry  consignment  accounts  show  a 
net  gain  of  $1287.14.  The  expense  account  (not  including  the 
partners'  salaries)  shows  a  loss  of  $3424.75.  What  is  each  partner's 
interest  in  the  business  at  closing?  How  will  A  be  affected  if 
each  partner's  salary  is  increased  to  $2500  ? 


262  PARTNERSHIP. 

35.  A  and  B  unite  in  conducting  a  summer  hotel,  on  the  follow- 
ing basis  :  1.  Each  is  to  receive  interest  at  the  rate  of  6%  per 
annum  on  his  investment ;  2.  A  is  to  receive  a  salary  of  $1000  and 
B  of  $800,  for  the  season  ;  3.  The  profit  or  loss  of  the  general  busi- 
ness is  to  be  divided  in  the  proportion  of  A  |,  B  -J ;  the  profit  or 
loss  of  the  livery  business  attached  thereto  in  the  proportion  of 
A  ^,  B  f ;  the  profit  or  loss  of  the  bathing  business  in  the  propor- 
tion of  A  -J-,  B  J.  A  invests  an  average  of  $10150  for  four  months, 
and  B  an  average  of  $6750  for  the  same  time.  At  the  close  of 
the  business  the  accounts  showing  loss  and  gain  stand  as  follows: 

Outgo.          HOTEL.        Income.  Outgo.      LIVERY.    Income. 

15150.75  |  25175.19         1592.75  |  3279.50 

Outgo.   BATHING.  Income. 


759.12     I     1275.30 

There  is  besides  an  item  of  service  amounting  to  $375,  which 
at  the  time  could  not  be  easily  apportioned  in  the  charges,  and 
which,  of  course,  does  not  appear  in  the  above  outgoes.  It  is 
agreed  that  this  item,  as  also  the  sums  severally  due  the  partners 
for  interest  and  salaries,  shall  be  charged  to  the  several  depart- 
ments of  the  business  in  proportion  to  the  net  gains.  There  is, 
also,  an  inventory  in  the  livery  business  amounting  to  $429.33. 
How  much  clear  gain  from  all  sources  will  each  partner  get  out  of 
the  business. 

36.  A,  B,  and  0  are  equal  partners  in  a  mill,  each  to  receive 
6%  per  annum  interest  on  his  average  investment.  C  is  to  super- 
intend the  business  and  receive  therefor  a  yearly  salary  of  $3000  ; 
B  keeps  a  store  at  which  the  operatives  trade,  and  is  to  pay  to  A 
and  C  5%  on  sales  to  operatives.  A  negotiates  the  products  of  the 
mill,  for  which  he  is  allowed  10$  on  the  net  profits  as  existing 
before  his  percentage  is  taken.  A's  average  investment  for  the 
year  is  $9750;  B's  $5750  ;  C's  $5000.  Leaving  out  the  interest, 
salary  and  percentages,  the  net  gain  for  the  year  is  $15000.  B's 
sales  to  operatives  amount  to  $1575.  What  share  of  the  $15000  is 
each  partner  entitled  to  ? 

87.  A  owns  a  business,  the  good  will  of  which  is  estimated  at 
$10000,  and  the  stock  on  hand  at  $15000.  B  and  C  agree  to. 
unite  with  him  on  the  following  conditions :  B  to  invest  $25000 


PARTNERSHIP.  263 

cash,  and  C  to  devote  his  entire  time  to  the  business,  for  which 
he  is  to  receive,  in  addition  to  his  interest,  an  annual  salary  of 
$1000.  The  capital  is  to  be  kept  intact,  and  no  interest  to  be 
allowed  therefor.  The  gain  or  loss  to  be  divided  equally  between 
the  three  partners.  At  the  end  of  the  year  the  resources,  includ- 
ing good  will,  book  accounts,  notes,  inventories,  etc.,  but  not  in- 
cluding amounts  drawn  by  the  partners,  amount  to  $67000,  and 
the  liabilities  to  outside  parties,  to  $10500.  C  has  drawn  out 
during  the  year  $2500  ;  B,  $1575  ;  A,  $2000.  Of  the  resources 
above  named  there  are  bad  debts  not  to  be  counted,  amounting  to 
$575.  What  is  the  condition  of  each  partner's  account? 

tfS.  A,  B,  and  C  are  partners  in  business,  investing  as  follows  : 
A,  $4000;  B,  $6000;  C,  $8000.  The  partners  are  to  share  the 
profits  and  losses  in  proportion  to  their  investments.  Each  is 
entitled  to  compensation  for  services  at  the  rate  of  $150  per  month, 
payable  at  the  end  of  each  month  and  not  to  bear  interest.  In 
case  that  either  partner  shall  draw  a  greater  amount  than  shall  at 
the  time  be  due  him  for  services,  he  shall  be  charged  interest  upon 
such  overdraft  at  the  rate  of  \%  per  month  for  the  length  of  time 
such  overdraft  continues.  At  the  end  of  the  year  B  and  C  purchase 
the  interest  of  A,  and  in  the  payment  therefor,  it  is  desired  that 
the  remaining  members  shall  so  invest  that  their  interests  shall 
be  equal.  It  is  mutually  agreed  that  the  "good  will"  of  the 
business  shall  be  valued  at  $3000  in  the  final  settlement.  It  is 
also  agreed  that  a  discount  of  b%  shall  be  allowed  upon  all  un- 
collected  accounts  as  a  fund  to  meet  bad  debts  and  costs  for  col- 
lecting. A  statement  of  the  business  previous  to  closing  shows 
the  following  results  :  merchandise,  horses,  wagon,  office  fixtures, 
and  cash  on  hand,  $12410 ;  sundry  debtors,  $17030 ;  sundry 
creditors,  $4050 ;  expense  account  (not  including  partners' 
salaries),  $2400  ;  profit  on  merchandise  sold,  $15290.  A  withdrew 
on  account  of  salary  Apr.  1,  $450  ;  July  1,  $300  ;  Oct.  1,  400. 
B  withdrew  Mar.  1,  $400 ;  Apr.  1,  $150 ;  June  1,  400 ;  Oct.  1, 
$800;  Dec.  1,  $500.  C  withdrew  Apr.  1,  $600;  July  1,  $700; 
Oct.  1,  $600  ;  Nov.  1,  $200.  How  much  must  B  and  C  each  in- 
vest or  pay  A,  and  how  should  the  books  of  the  new  firm  be  opened  ? 
(Condensed  from  "The  Book-Keeper.") 

NOTE. — B  and  C,  not  desiring  to  have  the  new  books  encumbered  with 
the  contingent  accounts  of  "good  will"  and  "reserve  fund/'  closed  these 
accounts  after  a  settlement  was  made  with  A. 


NATIONAL     BANKS. 


DEFINITIONS. 

511.  A  National  Bank  is  a  bank  organized  under  the  laws 
of,  and  chartered  by,  the  United  States. 

1.  Associations  for  the  purpose  of  carrying  on  the  business  of  banking 
may  be  formed  by  any  number  of  persons,  not  less  in  any  case  than  five 
(R.  S.  §5133). 

2.  No  association  shall  be  organized  with  a  less  capital  than  $100,000 ; 
except  that  banks  with  a  capital   of  not  less  than  $50,000  may,  with  the 
approval  of  the  Secretary  of  the  Treasury,  be  organized  in   any  place  the 
population  of  which  does  not  exceed  6,000  inhabitants.     No  association  shall 
be  organized  in  a  city  the  population  of  which  exceeds  50,000  persons  with  a 
less  capital  than  $200000  (R.  S.  §  5138).     The  capital  stock  shall  be  divided 
into  shares  of  $100  each. 

3.  Every  national  bank,  before  it  shall  be  authorized  to  commence  busi- 
ness, shall  transfer  and  deliver  to  the  Treasurer  of  the  United  States,  any 
U.  S,  registered  bonds,  bearing  interest,  to  an  amount  not  less  than  one-third 
of  the  capital  stock  paid  in  ;  except  that  national  banks  having  a  capital  of 
$150,000  or  less,  shall  not  be  required  to  deposit  U.  S.  bonds  in  excess  of  one- 
fourth  of  their  capital  stock,  as  security  for  their  circulating  notes.    (Act  of 
July  12,  1882.) 

4.  National  banks  are  authorized  to  discount  and  negotiate  notes,  drafts, 
etc. ;  to  receive  deposits  ;  to  buy  and  sell  exchange,  coin  and  bullion  ;  to  loan 
money  on  personal  security  ;  and  to  issue  circulating  notes  (R.  S.  §  5136). 

5.  National  banks  are  prohibited  from  making  loans  on  real  estate  (R.  S. 
§  5137),  or  on  security  of  their  own  shares  of  capital  except  to  secure  debts 
previously  contracted  (R.  S.  §  5201). 

Real  estate  purchased  or  mortgaged  to  secure  a  pre-existing  debt  shall 
not  be  held  for  a  longer  period  than  five  years  (R.  S.  §5137). 

They  are  also  prohibited  from  making  loans  to  one  person  or  association, 
excepting  on  business  paper  representing  actually  existing  value  as  security, 
in  excess  of  one-tenth  of  the  capital  of  the  bank  (R.  S.  §  5200). 

6.  The  stockholders  of  a  national  bank  are  individually  liable  (equally 
and  ratably,  and  not  one  for  another)  for  an  amount  equal  to  the  par  value 
of  the  capital  stock  held  by  them. 


DEFINITIONS.  265 

Circulation.  Upon  a  deposit  of  registered  bonds,  the 
association  making  the  same  shall  be  entitled  to  receive  from  the 
Comptroller  of  the  Currency  circulating  notes  of  different  denomi- 
nations (19O),  in  blank,  equal  in  amount  to  ninety  per  centum 
of  the  current  market  .value  not  exceeding  par,  of  the  United 
States  bonds  so  transferred  and  delivered,  and  at  no  time  shall 
the  total  amount  of  such  notes  issued  to  any  such  association 
exceed  ninety  per  centum  of  the  amount  at  such  time  actually 
paid  in  of  its  capital  stock. 

1.  Any  national  bank  desiring  to  decrease  its  circulation,  in  whole  or  in 
part,  may  deposit  lawful  money  (specie  or  legal  tenders)  with  the  Treasurer 
of  the  United  States  in  sums  of  not  less  than  $9,000,  and  withdraw  a  propor- 
tionate amount  of  bonds  held  as  security  for  such  notes. 

No  national  bank  which  makes  any  deposit  of  lawful  money  in  order  to 
withdraw  its  circulating  notes,  shall  be  entitled  to  receive  any  increase  of  its 
circulation  for  the  period  of  six  months  from  the  time  it  made  such  deposit. 
Not  more  than  $3,000,000  shall  be  deposited  during  any  calendar  month  for 
this  purpose.  (Act  of  July  12,  1882.) 

2.  The  State  bank  circulation  wholly  ceased  after  Congress  had  imposed 
a  penalty  of  10^  in  the  form  of  a  tax  every  time  it  should  be  issued.    This  act 
took  effect  Aug.  1, 1866. 

513.  Redemption.— The  circulating  notes  of  national  banks 
are  redeemed  in  lawful  money  by  the  banks  which  issued  them 
and  by  the  Treasurer  of  the  United  States  at  Washington,  D.  C. 

1.  Section  3  of  the  act  of  June  20,  1874,  provides  that  every  national  bank 
shall,  at  all  times,  keep  and  have  on  deposit  in  the  Treasury  of  the  United  States 
in  lawful  money  of  the  United  States,  a  sum  equal  to  5%  of  its  circulation,  to 
be  held  and  used  for  the  redemption  of  such  circulation. 

2.  "  Section  5222  of  the  Revised  Statutes  requires  that  all  national  banks 
which  go  into  voluntary  liquidation  shall,  within  six  months  thereafter, 
deposit  in  the  Treasury  an  amount  of  lawful  money  equal  to  the  amount  of 
their  circulating  notes  outstanding.     The  law  also  requires  that  full  provi- 
sion shall  be  made  for  the  redemption  of  the  circulating  notes  of  any  insol- 
vent bank  before  a  dividend  is  made  to  its  creditors.     Thus  it  will  be  seen 
that  no  association  can  close  up  its  business  without  first  providing  for  the 
payment  of  all  its  circulating  notes,  and  that  the  amount  deposited  for  their 
redemption  must  remain  in  the  Treasury  until  the  last  outstanding  note 
shall  have  been  presented.     It  is  therefore  plain  that  the  government,  and 
not  the  bank,   receives  all  the  benefit  arising  from  lost  or  unredeemed 
circulating  notes." 


#66  NATIONAL    BANKS. 

514.  Official  Eeport  of  a  National  Bank. 

T3EPORT  OF  THE  CONDITION  OP  "THE  MERCHANTS'  NA- 
.Lt  TIONAL  BANK,"  at  New  York,  in  the  State  of  New  York,  at  tlie 
close  of  business  on  the  llth  day  of  March,  1881 : 

RESOURCES. 

Loans  and  discounts $6,443,761  75 

Overdrafts 2,417  71 

U.  S.  bonds  to  secure  circulation  (par  value) 400,000  00 

U.  S.  bonds  on  hand  (par  value) , 95,000  00 

Other  stocks,  bonds,  etc 9,000  00 

Due  from  other  National  banks 265,104  90 

Due  from  State  and  private  banks  and  bankers 158,515  75 

Banking  house $181,000  00 

Other  real  estate , 25,000  00  206,000  00 

Current  expenses  and  taxes  paid 15,748  72 

Premiums  paid 14, 187  50 

Checks  and  other  cash  items 87,440  57 

Exchanges  for  Clearing  House  (546) 3,987,982  71 

Bills  of  other  banks 45,418  00 

Fractional  paper  currency,  nickels,  and  cents 970  00 

Specie,  viz. :  Gold  coin $280,578  39 

Gold  Clearing  House  Certificates  (547,  15).  ...  730,000  00 

Silver  coin 4,217  60  1,014,795  99 

Legal  tender  notes  (1 89) 796,192  00 

Redemption  fund  with  U.  S.    Treasurer  (5%    of  circulation) 

(513,  1) 18,000  00 

Total $13,560,535  60 

LIABILITIES. 

Capital  stock  paid  in $2,000,000  00 

Surplus  fund 389,850  91 

Undivided  profits 346,361  55 

National  bank  notes  outstanding 360,000  00 

State  bank  circulation  outstanding 2,689  00 

Dividends  unpaid 3,320  25 

Individual  deposits  subject  to  check $5,417,189  10 

Demand  certificates  of  deposit 6,124  36 

Certified  checks 1,567,905  28 

Cashier's  checks  outstanding 280,699  59  7,271,918  33 

Due  to  other  National  banks 2,543,987  11 

Due  to  State  and  private  banks  and  bankers 642,408  45 

Totai. .  $13,560,535  60 


NATIONAL    BANKS.  267 

515.  Reserve. — The  national  banks  in  the  reserve  cities* 
are  required  by  law  to  hold  a  lawful  money  reserve  of  25%  of 
their  deposits  ;  all  other  national  banks  15%.     The  excess  above 
legal  requirements  is  called  "surplus  reserve." 

The  reserve  is  made  up  of  specie,  legal-tender  notes  (189),  U.  S.  certifi- 
cates of  deposit,  balances  due  from  reserve  agents,  and  the  5%  redemption 
fund,  with  the  U.  S.  Treasurer  (513,  1). 

516.  Surplus  Fund. — The  law  provides  that    a    surplus 
fund   shall   be   accumulated,  by   setting  aside,  before  the  usual 
semi-annual   dividend  is   declared,    one-tenth  part   of    the    net 
profits  of  the  bank  for  the  preceding  half-year,  until  the  surplus 
fund  shall  amount  to  20%  of  its  capital  stock. 

517.  Taxation. — The  national  banks  pay   to  the    United 
States  a  tax  of  1%  annually  upon  the  average  amount  of  their 
notes  in  circulation,  \%  annually  upon  the  average  amount  of 
their  deposits,  and  \%  annually  upon  the  average  amount  of  cap- 
ital not  invested  in  U.  S.  bonds. 

The  banks,  other  than  national,  pay  taxes  to  the  United  States  on 
account  of  their  circulation,  deposits,  and  capital,  at  the  same  rates  as  are 
paid  by  the  national  banks. 

EXAMPLES. 

518.  1.  Oct.  2, 1879,  the  number  of  notes  held  by  the  national 
banks  was  808,269,  and  the  total  amount  $875,013,107.     What 
was  the  average  amount  of  each  note  discounted  ? 

2.  The  impairment  of  the  capital  stock  ($300000)  of  an  insol- 
vent national  bank  was  $216000.  What  was  the  rate  per  cent, 
of  the  assessment  made  upon  the  stockholders  for  the  purpose  of 
making  good  the  deficiency  (511,  6)  ?  How  much  was  Mr.  A. 
obliged  to  pay,  who  owned  80  shares  ? 

8.  What  amount  of  bank  notes  is  issued  to  a  national  bank 
that  deposits  $780000  in  U.  S.  bonds  to  secure  circulation 
(512)  ?  How  much  is  its  redemption  fund  (513,  1)  ? 

4-  A  national  bank,  desiring  to  reduce  its  circulation,  deposits 
with  the  Treasurer  of  the  United  States  $27000  in  legal-tenders, 

*  The  reserve  cities  are  New  York,  Boston,  Philadelphia,  Baltimore,  Albany,  Pitts- 
burgh, Washington,  New  Orleans,  Louisville,  Cincinnati,  Cleveland,  Chicago,  Detroit,  Mil- 
waukee, Saint  Louis,  and  San  Francisco. 


268  NATIONAL    BANKS. 

and  sells  the  bonds  withdrawn  (512,  2)  in  the  market  at  118|. 
What  were  the  proceeds  ? 

5.  The   circulation  of  a  national  bank   having  a  capital  of 
$150000  is  $57600;  what  is  the  remaining  amount  of  circulation 
which  it  may  call    for    by   depositing    the    necessary    amount 
of  bonds   (512)?    What  is  the   par  value  of  the   bonds  now 
on  deposit?     What  additional  amount  of  bonds  will  the  bank 
be  required  to  deposit  if  the  circulation   is  increased   to  the 
maximum  ? 

6.  How  much  is  the   redemption    fund    of    a  bank  whose 
circulation  is    $427500?      What    is   the   amount  of   bonds   on 
deposit  to  secure  its  circulation  ? 

7.  The  New   York  associated  banks,  according  to  the  state- 
ment of  Saturday,  Mar.  25,  1882,  held  $58,602,100  in  specie 
and  $16,150,900  in  legal-tenders.      Their  deposits  on  the  same 
date  were  $285,659,600.     What  was  the  excess  of  reserve  (515) 
above  legal  requirements  ? 

8.  Oct.  1,  1881,  the  national  banks  of  Boston  had  $8.286,182 
in  specie,  $3,457,379  in  legal-tenders,  $75,000  in  U.  S.  certifi- 
cates of  deposit,    $11,735,499   due  from  reserve   agents,  and  a 
redemption  fund  with  U.   S.   Treasurer  of  $1,603,628.      What 
was    the    ratio    of    the    reserve    to    the    deposits,    which  were 
$95,776,386?     What  amount  of 'reserve  was  required?     What 
was  the  surplus  reserve  ? 

9.  What  amount  of  reserve  was  required   by  the  national 
banks  of  the  State  of  Maine,  their  deposits  being  $9,558,878  ? 

10.  The  net  earnings  of  a  bank,  whose  surplus  (516)  is  less 
than  20%  of  its  capital  ($300000),  are  $10475.38.     What  amount 
must  be  carried  to  the  surplus  account,  and  what  are  the  undivided 
profits  after  declaring  a  dividend  of  3%  ? 

11.  What    is    the    semi-annual   tax    (517)  upon    a    banker 
whose  capital  is  $5358,  and  whose  average  deposits  are  $18368  ? 

12.  What   is  the   semi-annual    tax    upon    a    national    bank 
whose  average  circulation  is  $462,730,  average  deposits  $1,185,952, 
capital  $1,500,000  ? 

13.  A  bank   having  a  capital  of  $250,000,    and  a  surplus 
of  $50,000,    for  a  period   of  six   months,    earned  $58693,  and 
declared  a  dividend  of  $30000.    What  was  the  rate  of  the  divi- 
dend ?     The  dividend  is   what  %  of  the  capital  and   surplus  ? 
The  net  earnings  are  what  %  of  the  capital  and  surplus  ? 


SAVINGS     BANKS. 


DEFINITIONS. 

519.  Savings  Banks  are  institutions  for  the  deposit  and 
safe  keeping  of  small  sums  of  money.     They  are  designed  to 
encourage  thrift  and  economy  among  the  working  classes. 

520.  Interest  is  usually  declared  Jan.  1st  and  July  1st  of 
each  year,  and  when  declared  is  carried  at  once  to  the  credit  of 
each  depositor  on  the  books  of  the  bank,  where  it  stands  as  a 
deposit,  and  is  entitled  to  interest  the  same  as  any  other  deposit. 
Savings  banks,  therefore,  pay  compound  interest. 

No  interest  is  allowed  on  the  fractional  parts  of  a  dollar,  nor 
is  any  interest  allowed  on  any  sum  withdrawn  previous  to  the 
first  day  of  January  or  July,  for  the  period  which  may  have 
elapsed  since  the  last  dividend. 

521.  Deposits  are  practically  payable  on  demand,  though 
the  right  to  require  a  notice  of  60  or  90  days  is  reserved. 

In  some  savings  banks,  deposits  commence  to  draw  interest 
Jan.  1st,  April  1st,  July  1st,  and  Oct.  1st ;  in  others,  deposits 
made  on  or  before  the  first  of  any  month  draw  interest  from  the 
first  days  of  those  months  respectively. 

522.  According  to  the  laws  of  the  State  of  New  York, 

No  person  shall  have  a  deposit  larger  than  the  sum  of  three  thousand 
dollars,  exclusive  of  accrued  interest,  unless  such  deposit  was  made  prior 
to  the  passage  of  the  act  (May  17,  1875),  or  pursuant  to  the  order  of  a 
court  of  record,  or  of  a  surrogate. 

Savings  banks  are  restricted  to  5%  per  annum  regular  interest  or  divi- 
dend. They  must,  however,  declare  an  extra  dividend  at  least  once  in  three 
years,  when  their  surplus  earnings  amount  to  15$  of  their  deposits. 

Saving's  banks  are  allowed  to  pay  interest  on  all  sums  deposited  during 
the  first  ten  days  of  January  and  July,  and  the  first  three  days  of  April  and 
October  from  the  first  of  those  months  respectively. 


70  SAVINGS    BANKS. 


EXAMPLES. 


523.  Perform  the  following  examples  according  to  both 
methods  mentioned  in  Art.  521.  Where  no  rate  is  mentioned, 
4%  is  understood. 

1.  Mr.  A.  deposited  in  a  savings  bank,  Jan.  1,  1882,  $145. 
How  much  interest  should  be  credited  to  him  July  1,  1882  ? 

OPERATION. 

145  ANALYSIS.  —  In  any  savings  bank,  lie  would  be  credited  for 

02        the  interest  of  $145  from  Jan.  1  to  July  1,  or  6  mo.  at  4%  per  an- 
num.    k.%  per  annum  is  equivalent  to  2%  for  6  mo. 


2.  Mr.  B.  deposited  in  a  savings  bank  Mar.  29,  1880, 
How  much  interest,  at  5$,   should  be  credited  to  him  July  1, 
1880  ?  Ans.  $2.75. 

OPEBATION.  ANALYSIS.—  He   is  entitled  to  the  interest  of  $220 

*%•         from  Apr.  1  to  July  1,  or  3  mo.,  at  5^  per  annum.     5f/0 
55  —  £%.         per  annum  is  equivalent  to  \\%  for  3  mo.     ^\%  is  found 


o 
A 


as  in  the  operation. 


S.  A  person  deposited  Dec.  30,  1881,  $150;  Feb.  20,  1882, 
$40  ;  April  1,  1882,  $120  ;  May  30,  1882,  $60.  What  amount 
was  due  July  1,  1882,  nothing  having  been  withdrawn  ? 

ANALYSIS.  —  If  interest  begin  on  the  first  of  each  quarter,  the  first 
deposit,  $150,  will  draw  interest  from  Jan.  1,  or  for  6  mo.  ;  the  second  and 
third  deposits,  $160,  will  draw  interest  from  April  1,  or  for  3  mo.  ;  the  last 
deposit,  made  May  30,  will  draw  no  interest  July  1. 

If  interest  begin  on  the  first  of  each  month,  the  first  deposit,  $150,  will 
draw  interest  from  Jan.  1,  or  for  6  mo.  ;  the  second  deposit,  $40,  made 
Feb.  20,  will  draw  interest  from  March  1,  or  for  4  mo.  ;  the  third  deposit,  $120, 
made  April  1,  will  draw  interest  from  April  1,  or  3  mo.;  the  fourth  deposit, 
$100,  made  May  30,  will  draw  interest  from  June  1,  or  for  1  mo. 

4-  The  following  deposits  were  made  in  a  savings  bank  : 
July  1,  1881,  $100  ;  July  16,  $40  ;  Aug.  1,  $75  ;  Aug.  29,  $45  ; 
Sept.  30,  $75  ;  Oct.  28,  $200  ;  Nov.  25,  $30  ;  Dec.  31,  $100.  What 
was  due  Jan.  1,  1882  ? 

5.  How  much  interest  was  due  on  the  following  account 
July  1,  1883  ?  Deposits,  Oct.  1,  1881,  $200  ;  Dec.  31,  1881,  $160  ; 
Mar.  24,  1883,  $100. 


SAVINGS    BANKS. 


271 


6.  Mr.   A.  made  the  following  deposits  in  a  savings  bank: 
Jan.  1,   1879,  $100 ;    May  1,  1879,   $140 ;   June  30,  1879,  $40 ; 
Oct.  1,  1879,  $60 ;    Feb.  28,   1880,   $120 ;    June  30,   1880,  $45 ; 
Aug.  29,  1881,  $200.     What  was  the  balance  due  Jan.  1,  1882  ? 

7.  What  is  the  balance  of  the  following  account  July  1,  1879, 
interest  being  reckoned  at  Q%  until  July  1,  1877,  and  at  5%  there- 
after :     Deposits,   Oct.    14,   1876,   $200;    Mar.   30,   1878,   $135; 
April  1,  1879,  $90. 

8.  How  much  is  due  on  the  following  account  July  1,  1879, 
interest  being  reckoned  at  6%  until  Jan.  1,  1877,  and  at  5%  there- 
after :  Deposits,  Jan.  31,  1876,  $100  ;  Apr.  1, 1876,  $100  ;  Oct.  28, 

1878,  $30 ;    Nov.   30,   1878,   $30 ;    Feb.   1,   1879,   $25 ;    Mar.  1, 

1879,  $25. 

9.  What  is  the  balance  of  the  following  account  July  1,  1882  ? 
Balance  due  Jan.  1,  1882,  $103.     Deposits,  Jan.  28,  $40  ;  Mar.  30, 
$125  ;  May  26,  $80.     Drafts,  Feb.  20,  $20 ;  April  18,  $15  ;  May  3, 
$25  ;  June  16,  $100. 

ANALYSIS. — In  order  to  more  readily  determine  the  amounts  that  are 
entitled  to  interest,  arrange  the  account  in  the  following  form,  and  find  the 
balance  after  each  draft  or  after  two  or  more  drafts  made  without  any  inter- 
mediate deposit. 


Date. 

Deposits. 

Drafts. 

Balances. 

Jan.       1, 

103 

28, 

40 

Feb.     20, 

20 

123 

Mar.    30, 

125 

Apr.     18, 

15 

May       3, 

25 

208 

26, 

80 

June    16, 

100 

188 

The  smallest  balance  found  is  $123,  the  amount  remaining  on  deposit 
after  the  draft  of  Feb.  20  ;  of  this  balance,  $103  was  on  deposit  Jan.  1,  and  the 
remaining  $20  was  deposited  Jan.  28.  (It  is  the  custom  to  deduct  the  drafts 
from  the  last  deposits  made).  Since  the  balance  June  16,  $188,  is  less  than 
the  balance,  May  8,  $208,  it  is  evident  that  the  excess,  $20,  has  been  with- 
drawn, and  therefore  is  not  entitled  to  interest.  Of  the  $188,  interest  has 
already  been  allowed  on  $123,  and  the  remaining  $65,  it  is  seen  by  inspection, 
was  deposited  Mar.  30. 

If  interest  commence  the  first  of  each  quarter,  the  several  amounts  will 


SA  VINGS    BANKS. 

draw  interest  as  follows  :    $103  from  Jan.  1,  or  6  months  ;    $30,  deposited 
Jan.  28,  and  $65  deposited  Mar.  30,  making  $85  from  April  1,  or  3  months. 

If  interest  commence  the  first  of  each  month,  the  several  amounts  will 
draw  interest  as  follows  :  $103  from  Jan.  1,  or  6  months  ;  $20,  deposited 
Jan.  28,  from  Feb.  1,  or  5  months ;  $65,  deposited  Mar.  30,  from  April  1,  or 
3  months. 

10.  What   is   the   balance  of  the  following  account  July  1  ? 
Balance  due  Jan.  1,  $30;    deposits,  Feb.  16,  $50;    Apr.  1,  $185. 
Drafts,  Mar.  12,  $60  ;  May  10,  $50  ;  June  20,  $60. 

11.  Find  the  balance  of  the  following  account,  Jan.  1,  1883. 
Deposits,  July  1,  1882,  $175  ;  Aug.  1,  $40  ;  Sept.  16,  $280.   Drafts, 
Oct.  18,  $90 ;  Nov.  27,  $125. 

12.  Balance  the  following  account,  Jan.   1,  1882.     Deposits, 
July  28,  1881,   $100;    Aug.  16,  1881,  $75;   Oct.  17,  1881,  $50; 
Oct.   30,   1881,    $20.      Drafts,   Sept.   30,   1881,   $25  ;    Nov.    30, 
1881,  $100. 

13.  Balance  the  following  Jan.  1,  1881.     Balance  due  July  1, 

1880,  $300.     Deposits  received,  Aug.   1,   $150  ;    Sept.   27,  $60 ; 
Oct.  12,  $325.     Drafts  paid,  July  16,  $150  ;   Sept.  1,  $150  ;  Nov. 
17,  $70 ;  Dec.  18,  $140. 

14.  What  is  the  balance  of  the  following  account  July  1, 1882  ? 
Balance  due  Jan.  1,  1882,  $364.48.     Deposits,  Jan.  24,  1882,  $50  ; 
Feb.  16,  1882,  $80 ;    Apr.  30,  1882,   $40  ;    June  28,  1882,  $100. 
Drafts,  Mar.  30,  1882,  $75  ;  May  19,  1882,  810. 

15.  How  much  is  due  on  the  following  account  Jan.  1,  1882  ? 
Deposits,  Dec.  16,  1880,  $300;    Feb.  25,   1881,   $100;    Mar.  16, 

1881,  $40 ;  July  1,  1881,  $25  ;  Sept.  24,  1881,  $50  ;  Dec.  30, 1881, 
$100.     Drafts,  June  18,  1881,  $75  ;  Nov.  13,  1881,  $30. 

16.  What  is  the  balance  of  the  following  account  July  1,  1882  ? 
Deposits,  Jan.  3  (as  Jan.  1),  1881,  $500;  Mar.  30,  1881,  $90;  Oct. 
1,  1881,  $160  ;    Feb.  20,  1882,  $80  ;    Mar.  28,  1882,  $40.    Drafts, 
July  20, 1881,  $100  ;  Jan.  2  (as  Jan.  1),  1882,  $40  ;  June  1, 1882,  $60. 

17.  How  much  was  due  July  1, 1882,  on  the  following  pass-book? 

Dr.       FRANKLIN  SAVINGS  BANK  in  account  "with  F.  G.  SNOOK.       Or. 


1881. 

1881. 

Jan.     1 

Four  Hundred  Dollars. 

400 

Aug.  1 

Two  Hundred  Dollars. 

200 

Mar.   15 

Ninety  Dollars. 

90 

1882. 

1881. 

Interest  to  July. 

* 

*# 

Jan.  16 

One     Hundred     and 

Sept.  16 

Two  Hundred  Dollars. 

200 

Sixty  Dollars. 

160 

1882. 

Interest  to  January. 

* 

*# 

Junel 

Eighty  Dollars. 

80 

Feb.   27 

Two  Hundred  and  Sixty  Dollars. 

230 

Mar.    8 

One  Hundred  Dollars. 

100 

LIFE     INSURANCE. 


DEFINITIONS. 

524.  Life  Insurance  is  a  contract  by  which  a  company  (the 
insurer),  in  consideration  of  certain  payments,  agrees  to  pay  to  the 
heirs  of  a  person,  when  he  dies,  or  to  himself,  if  living  at  a  specified 
age,  a  certain  sum  of  money. 

Life  Insurance  Companies  may  be  classified  according  to  principles  of 
organization  the  same  as  Fire  Insurance  Companies  (31)1). 

Of  the  31  Life  Insurance  Companies  doing  business  in  the  State  of  New 
York  in  1879,  2  were  Stock  (392),  17  Mixed  (394)  (Stock  and  Mutual),  and 
12  purely  Mutual  (393).  Their  assets  Dec.  31,  1879,  were  $401,515,793  ;  sur- 
plus as  regards  policy  holders,  $65,277,722  ;  number  of  policies  in  force,  595,486, 
insuring  $1,439,961,163. 

Of  the  companies  chartered  by  the  State  of  New  York  and  doing  business 
in  1879, 10  were  Mixed  (Stock  and  Mutual),  and  2  were  purely  Mutual. 

525.  The  principal  kinds  of  policies  issued  by  Life  Insurance 
Companies  are  the  following:    Ordinary  Life,  Limited  Pay- 
ment Life,  Endowment,  and  Annuity. 

Tontine  Investment,  Reserve  Endowment,  Convertible  Life,  Accelerative 
Endowment,  Yearly  Renewable,  and  other  special  policies  are  issued  by  some 
companies. 

526.  Ordinary  Life  Policies. — On  this  kind  of  policy,  a 
certain  premium  is  to  be  paid  every  year  until  the  death  of  the 
insured,  when  the  policy  becomes  payable  to  the  persons  named  in 
the  policy  as  the  beneficiaries. 

A  policy  of  this  kind  gives  more  insurance,  for  the  same  sum  of  money 
paid  annually,  than  any  other,  though  it  is  necessary  to  continue  the  payments 
longer ;  as  according  to  its  terms  the  payment  of  the  premiums  annually  con- 
tinues during  the  life-time  of  the  insured. 


374  LIFE    INSURANCE. 

527.  Limited  Payment  Life  Policies. — On  a  policy  of 
this  kind,  premiums  are  paid  annually  for  a  certain  number  of  years 
fixed  upon  at  the  time  of  insuring — or,   until  the  death  of  the 
insured,  should  that  occur  prior  to  the  end  of  the  selected  period. 
The  policy  is  payable  on  the  death  of  the  insured,  whenever  that 
may  occur. 

The  payments  on  this  class  of  policies  may  all  be  made  wliile  the  insured 
is  still  young,  or  in  active  business  ;  then  if  he  Jives  to  old  age  the  policy  is 
not  a  continual  expense,  bat,  on  the  contrary,  the  dividends  afford  a  yearly 
income  in  cash  ;  or  they  may  be  used  to  increase  the  amount  assured. 

These  policies  are  issued  with  single  payments,  or  with  5,  10,  15,  20,  or  25 
annual  payments. 

528.  A  Term  Life  Policy  is  an  agreement  to  pay  to  the 
representatives  of  the  insured  a  certain  sum  on  his  death,  provided 
that  event  happens  within  a  certain  fixed  term. 

529.  Endowment  Policies. — An  Endowment  Policy  pro- 
vides '(1)  insurance  during  a  stipulated  period,  payable,  like  that 
of  any  other  policy,  at  the  death  of  the  insured  should  he  die 
within  the  period;  and  (2)  an  endowment,  of  the  same  amount 
as  the  policy,  payable  at  the  end  of  the  period  if  the  insured  survive 
until  that  time. 

The  Endowment  Policy  gives  the  insured  the  advantage  of  a  limited  term 
as  to  payments ;  provides  insurance  during  the  period  in  which  his  death 
would  cause  most  embarrassment  to  his  family  ;  and,  if  he  lives  to  the  stipu- 
lated age,  the  amount  of  the  policy  is  paid  to  him  at  a  time  when  he  may 
need  it. 

An  Endowment  policy  is  a  combination  of  a  Term  Life  Policy  and  a  Pure 
endowment. 

These  policies  are  issued  for  endowment  periods  of  10,  15,  20,  25,  30,  or 
35  years,  and  may  be  paid  up  by  a  single  payment,  by  annual  premiums 
during  the  endowment  period,  or  by  5  or  10  annual  payments. 

530.  Annuity  Policies. — An  Annuity  Policy  secures  to  the 
holder  the  payment  of  a  certain  sum  of  money  every  year  during 
his  life-time.     It  is  secured  by  a  single  cash  payment. 

531.  A  Joint-Life  Policy  is  an  agreement  to  pay  a  certain 
sum  on  the  death  of  one  of  two  or  more  persons  named. 

532.  The  Reserve  of  life  insurance  policies  is  the  present 
value  of  the  amount  to  be  paid  at  death  less  the  present  value  of 
all  the  net  premiums  to  be  paid  in  the  future. 


DEFINITIONS.  275 

533.  The  Reserve  Fund  of  a  Life  Insurance  Company  is 
that  sum  in  hand  which,  invested  at  a  given  rate  of  interest  to- 
gether with  future  premiums  on  existing  policies,  should  be  suf- 
ficient to  meet  all  obligations  as  they  become  due.  It  is  the  sum 
of  the  separate  reserves  of  the  several  policies  outstanding. 

The  legal  rate  for  tlie  reserve  fund  according  to  the  laws  of  the  State  of 
New  York,  is  ±\%  ;  of  Massachusetts  4%. 


534.  A  Non-Forfeiting  Policy  is  one  which  does  not  become 
void  on  account  of  non-payment  of  premiums. 

1.  According  to  the  laws  of  the  State  of  New  York,  after  three  full  annual 
premiums  have  been  paid,  the  legal  reserve  of  the  policy,  calculated  at  the 
date  of  the  failure  to  make  the  payments,  shall,  on  surrender  of  the  policy 
within  six  months  after  such  lapse,  be  applied  as  a  single  payment  at  the 
published  rates  of  the  company  in  either  of  two  ways,  at  the  option  of  the 
assured.      (1)  To   the   continuance  of  the   full  amount  of  the  insurance  so 
long  as  such  single  premium  will  purchase  term  insurance  for  that  amount, 
or  (2)  to  the  purchase  of  a  non  -participating  paid-up  policy. 

2.  According  to  the  Massachusetts  limited  forfeiture  law  of  1880,  after  two 
full  annual  premiums  have  been  paid,  and  without  any  action  on  the  part  of 
the  assured,  the  net  value  (Massachusetts  standard)  of  the  policy  less  a  sur- 
render charge  of  8  %  of  the  present  value  of  the  future  premiums  which  the 
policy  is  exposed  to  pay  in  case  of  its  continuance,  shall  be  applied  as  a  single 
payment  to  the  purchase  of  paid-up  insurance. 

3  Certain  companies  voluntarily  apply  all  credited  dividends  to  the  continu- 
ance of  the  insurance  ;  others  voluntarily  apply  the  legal  reserve  to  the  pur- 
chase of  term  insurance  at  the  regular  rates. 

4.  In  some  companies,  all  limited  payment  life  policies  and  alt  endowment 
policies,  after  premiums  for  three  (or  two)  years  have  been  paid  and  the 
original  policy  is  surrendered  within  a  certain  time,  provide  for  paid-up  assur- 
ance for  as  many  parts  (tenths,  fifteenths,  twentieths,  etc.,  as  the  case  may 
be),  of  the  original  amount  assured,  as  there  shall  have  been  complete  annual 
premiums  received  in  cash  by  the  Company. 

535.  The  Surrender  Value  of  a  policy  is  the  amount  of  cash 
which  the  company  will  pay  the  holder  on  the  surrender  of  the 
policy.     It  is  the  legal  reserve  less  a  certain  per  cent,  for  expenses. 

The  Tontine  Investment,  Reserve  Endowment,  and  other  special  policies 
guarantee  to  the  policy-holder  a  definite  surrender  value  at  the  termination  of 
certain  periods. 

536.  The  Expectation  of  Life  is  the  number  of  years  which 
one  may  probably  live.     This  average  number  of  years  has  been 
determined  from  the  experience  of  Insurance  Companies. 


276 


LIFE    INSURANCE. 


TABLE  OF  RATES. 
537.  Annual  premium  for  an  Insurance  of  $1,000,  with  profits. 


LIFE  POLICIES. 

Payable  at  Death,  only. 

ENDOWMENT  POLICIES. 
Payable  as  Indicated,  or  ut  Death,  if  Prior. 

AGE. 

ANNUAL  PAYMENTS. 

AGE. 

In 
10 
Years. 

In 
15 
Years. 

In 
20 
Years. 

AGE. 

For  Life. 

10  Years. 

15  Years. 

20  Years. 

25 

$19  89 

$42  56 

$32  34 

$27  39 

25 

$103  91 

$66  02 

$47  68 

25 

26 

20  40 

43  37 

32  97 

27  93 

26 

104  03 

66  15 

47  82 

26 

27 

20  93 

44  22 

33  62 

28  50 

27 

104  16 

66  29 

47  98 

27 

28 

21  48 

45  10 

34  31 

29  09 

28 

104  29 

66  44 

48  15 

28 

29 

22  07 

48  02 

35  02 

29  71 

29 

104  43 

66  60 

48  33 

29 

30 

22  70 

46  97 

35  76 

30  36 

30 

104  58 

66  77 

48  53 

30 

31 

23  33 

47  98 

36  54 

31  03 

31 

104  75 

66  96 

48  74 

31 

32 

24  03 

49  02 

37  35 

31  74 

32 

104  92 

67  16 

48  97 

32 

33 

24  78 

50  10 

38  20 

32  48 

33 

105..  U 

67  36 

49  22 

33 

34 

25  56 

51  22 

39  09 

33  26 

34 

105  31 

67  60 

49  49 

34 

§5 

26  38 

52  40 

40  01 

34  08 

35 

105  53 

67  85 

49  79 

86 

30 

27  25 

53  63 

40  98 

34  93 

36 

105  75 

68  12 

50  11 

36 

87 

28  17 

54  91 

42  00 

35  83 

87 

106  00 

68  41 

50  47 

87 

38 

29  15 

56  24 

43  06 

36  78 

38 

106  28 

08  73 

50  86 

38 

39 

30  19 

57  63 

44  17 

37  78 

39 

106  58 

69  09 

51  30 

C9 

40 

31  30 

59  09 

45  33 

38  83 

40 

106  90 

69  49 

51  78 

40 

41 

32  47 

60  60 

46  56 

39  93 

41 

107  26 

69  92 

52  31 

41 

42 

33  72 

62  19 

47  84 

41  10 

,42 

107  65 

70  40 

52  89 

42 

43 

35  05 

63  84 

40  19 

42  34 

43 

108  08 

70  92 

53  54 

43 

44 

36  43 

65  57 

50  61 

43  64 

44 

108  55 

71  50 

54  25 

44 

45 

37  97 

67  37 

52  11 

45  03 

45 

109  07 

72  14 

55  04 

45 

48 

89  58 

69  26 

53  68 

46  50 

46 

109  65 

72  86 

55  91 

46 

47 

41  30 

71  25 

55  35 

48  07 

47 

110  30 

73  66 

56  89 

47 

48 

43  13 

73  32 

57  10 

49  73 

48 

111  01 

74  54 

57  96 

48 

49 

45  09 

75  49 

58  95 

51  50 

49 

111  81 

75  51 

59  15 

49 

50 

47  18 

77  77 

60  91 

53  38 

50 

112  68 

76  59 

60  45 

50 

1.  The  above  table  represents  the  maximum  rates  of  the  leading  New 
York  companies.     Surplus  premiums  or  dividends  are  returned  annually  com- 
mencing at  the  payment  of  the  second  premium. 

2.  Policies  which  do  not  share  in  the  dividends  of  the  company,  are  issued 
at  fixed  rates  15  to  20  %  less  than  the  above. 

3.  The  above  rates  are  for  annual  payments  only.     To  obtain  semi-annual 
payments,  add  4#  and  divide  by  2.     To  obtain  quarterly  payments,  add  Qfi 
and  divide  by  4. 


LIFE   INSURANCE. 


277 


538.    ANNUAL  REPORT  OF  A  LIFE  INSURANCE  Co., 
Jan.  1,  1882. 

Amount  of  assets,  Jan.  1,  1881 $36,889,011.66 

REVENUE  ACCOUNT. 

Premiums $6,003,036.16 

Interest  and  rents 2,033,650.00      8,036,686.16 

44,925,697.82 
DISBURSEMENT  ACCOUNT. 

Losses  by  death, including  Reversionary  additions 

to  same 1,569,854.22 

Endowments  matured  and  discounted 1,015,256.22 

Annuities,  dividends,  and  returned  premiums  on 

cancelled  policies 2,236,379.97 

Taxes  and  re-insurances 173,608.64        • 

Commissions,  brokerages,  agency  expenses  and 

physicians'  fees 626,253.30 

Office   and  law  expenses,  salaries,  advertising, 

printing,  etc 307,392.81      5,928,745.16 

88,006,059.66 

ASSETS. 

Cash  in  bank  and  on  hand 1,961,701.48 

Invested  in  j&nited  States,  New  York  City,  and 

othe^locks 14,556,192.94 

Real  estate\|rU 4,974,573.68 

Bonds  and  ^mortgages,  first  lien  on  real  estate.. .  15,313,278.95 

Temporary  loans  (secured  by  stocks,  market  value 

$1,300,000) 850,000.00 

Loans  on  existing  policies 621,403.02 

Quarterly  and  semi-annual  premiums  on  existing 

policies,  due  subsequent  to  Jan.  1,  1882. .  367,989.02 

Premiums  on  existing  policies  in  course  of  trans- 
mission and  collection 211,625.23 

Agents'  balances 22,199.23 

Accrued  interest  on  investments  Jan.  1,  1882. . .  317,989.11     38,996,952.66 

LIABILITIES. 
Adjusted  losses,  due  subsequent  to  Jan.  1,  1882.        225,662.64 

Reported  losses,  awaiting  proof,  etc 213,271.31 

Matured  endowments,  due  and  unpaid 32,780.98 

Premiums  paid  in  advance 16,543.25 

Reserve  for  re-insurance  on  existing  policies  at 

4i  per  cent 30,682,025.00    31,170,283.18 

Surplus  at  4|  per  cent 7,826,669.48 

38,996,952.66 


278  LIFE   INSURANCE. 


EXAMPLES. 

539.     1.  Find  the  amount  of  premium  for  an  ordinary  life 
policy  (526,  537)  of  $5000,  issued  to  a  person  35  years  of  age. 

2.  What  is  the  first  annual  premium  of  a  life  policy  of  $6000, 
issued  to  a  person  30  years  old,  $1.00  being  charged  for  the 
policy  ? 

NOTE. — The  policy  fee  is  added  to  the  first  premium  only. 

3.  Find  the  annual  premium  for  a   20-payment  life   policy 
(527,  537)  of  $4000,  issued  to  a  person  28  years  old. 

4.  What  annual  premium  must  be  paid  for  a  20-year  endow- 
ment policy  (529)  of  $8000,  age  of  the  insured  at  nearest  birth- 
day, 40  years  ?     If  the  insured  dies  during  the  tenth  year,  how 
much  more  would  have  been  paid  than  if  he  had  been  insured  on 
the  ordinary  life  plan  ? 

5.  What  is  the  average  daily  cost  of  a  life  policy  for  $1000,  no 
allowance  being  made  for  probable  dividends,  insurance  commenc- 
ing at  age  25  ?    At  35?     At  45? 

6.  How  much  must  a  person,  aged  35,  lay  aside  weekly  to 
secure  a  life  policy  of  $1000,  payable  in  20  annual  payments  ? 

7.  When  40  years  old,  a  person  took  out  a  20-year  endowment 
policy  of  $10000.     He  survived   the  endowment  period.      How 
much  less  did  he  receive  than  he  paid  as  premiums,  not  reckon- 
ing interest  ? 

8.  Mr.  A.  when  26  years  old  took  out  an  ordinary  life  policy 
of  $20000.     He  died  aged  41  years  2  months.     How  much  more 
did  his  heirs  receive  than  had  been  paid  as  premiums,  no  allow- 
ance being  made  for  interest  ? 

9.  In  the  above  example,  supposing  money  to  be  worth  6% 
(simple  interest),  what  was  the  net  gain  of  the  above  insurance  ? 

10.  The  annual  premium,  without  profits,  on  a  life  policy  of 
$10000  at  age  35  is  $222.     How  much  would  it  be  necessary  to 
invest  at  6%  interest  to  secure  the  payment  of  the  annual  pre- 
mium ?    How  much  would  the  insured  leave  his  family  at  his 
death  ? 

11.  A  gentleman,  age  30,  insures  his  life  for  $20000,  ordinary 
life  plan.     How  much  must  he  place  in  trust  so  that  the  interest 
at  5%  will  be  sufficient  to  pay  the  premiums  on  the  policy  ?     At 
his  death,  how  much  does  he  leave  his  family  ? 


LIFE    IXSURANCE.  279 

12.  Mr.  C.  when  25  years  of  age  secured  a  20-year  endowment 
policy  of  $6000  ;   when  he  was  30  years  of  age,  he  obtained  an 
ordinary  life  policy  of  $4000 ;   when  35  years  of  age,  he  toot  out 
a  20-payment  life  policy  of  $10000.     What  was  the  total  annual 
premium  after  taking  the  last  policy  ? 

13.  Suppose  Mr.  C.  had  died  at  the  age  of  40-J-  years,  how  much 
more  would  his  heirs  receive  than  had  been  paid  as  premiums  ? 

14-  A  single  premium  for  an  assurance  of  $1000,  without  profits, 
for  a  person  32  years  of  age,  is  $300.  What  would  be  the  excess  of 
the  assurance  over  the  amount  produced  by  placing  the  money  at 
compound  interest  (341)  at  4%,  supposing  the  insured  to  live  20 
years?  30  years  ?  What  would  be  the  excess  of  the  amount  pro- 
duced by  the  money  at  interest  at  5%  over  the  assurance  in  30  years  ? 

15.  Mr.  B.,  age  40,  has  $10000  at  interest  at  6$,  which  he  in- 
tends to  leave  his  family.    What  will  this  amount  to  at  compound 
interest  (341)  in  25  years  at  6%  ?    How  much  will  he  leave  his 
family  if  he  takes  out  a  life  policy  and  pays  the  premium  with  the 
interest  on  his  investment  of  $10000  ? 

16.  Mr.  A.,  aged  30,  secures  an  ordinary  life  policy,  annual 
premium  $100.     How  much  more  would  his  heirs  receive  from  the 
insurance  company  than  from  the  money  at  compound  interest 
(34:2)  at  5#,  should  he  die  at  the  age  of  32?    Of  40  ?    Of  50? 
At  about  what  age  would  the  amount  received  from  the  money  at 
interest  exceed  the  assurance  ? 

17.  What  is  the  semi-annual  premium  (537,  3)  on  a  20-year 
endowment  policy  for  $6000,  age  32  ?     The  quarterly  premium  ? 

18.  Mr.  A.,  who  will  be  35  years  of  age  July  1,  takes  out  Apr.  1 
a  20-payment  life  policy  for  $10000,  premium  payable  semi-annu- 
ally.     Mr.  B.,  of  the  same  age,  takes  out  Apr.  1  the  same  kind  of 
policy  for  $5000,  and  Oct.  1,  another  policy  of  the  same  kind  for 
$5000,  premium  payable  annually.     How  much  less  does  Mr.  B. 
pay  as  premium  each  year  than  Mr.  A.  ?     (537,  3.) 

19.  An  ordinary  life  policy  issued  at  age  35  for  $10000  has,  at 
age  45,  a  4%  reserve  of  $1262.60.     How  much  non-participating 
paid-up  insurance  will  this  amount  purchase,  the  single  premium 
rate  per  $1000  at  age  45  being  $475.44  ? 

20.  In  the  statement,  Art,  538,  the  surplus  is  what  per  cent, 
of  the  reserve  required  by  the  State  of  New  York  ?   The  net  assets 
(the  total  assets  less  the  first  four  items  of  the  liabilities)  are  what 
per  cent,  of  the  reserve  ? 


GENERAL    AVERAGE. 


DEFINITIONS. 

540.  If,  in  time  of  danger  or  distress,  any  loss  or  expense  is 
voluntarily  incurred  for  common  safety  of  vessel,  freight,  and 
cargo,  such  loss  or  expense  is  made  good  by  a  "  General  Aver- 
ags  ; "  the  amount  or  value  of  such  loss  or  expense  being  assessed 
upon  the  value  of  all  interests  involved  and  benefited. 

All  other  losses  and  expenses  are  of  a  "Particular  Average" 
nature,  and  are  to  be  borne  by  the  specific  interests  to  which  they 
apply. 

541.  The  losses  and  expenses  constituting  general  average  are 
as  follows : 

1.  Jettison,  or  throwing  overboard  of  cargo  to  lighten  the 
ship  ;  damage  to  cargo  by  water  going  down  the  hatches  during 
jettison ;  damage  by  chafing  or  breaking  after  jettison ;  freight  on 
cargo  jettisoned. 

2.  Sacrificing  ship's  materials,  as  the  cutting  away  of  masts, 
spars,  etc.     One-third  of  the  cost  of  repairs  of  ship's  materials  is 
a  special  charge  on  the  ship,  as  the  new  work  is  considered  better 
than  the  old.     No  deduction  is  made  for  anchors. 

3.  Expense  of  floating  a  stranded  ship. 

4.  Expense  of  entering  a  port  of  refuge,   either  to  repair 
damage  which  renders  it  dangerous  to  remain  at  sea,  whether  such 
damage  were  caused  by  accident  or  sacrifice  ;  or  otherwise  to  avert 
a  common  danger. 

5.  Expense  of  discharging  cargo  for  the  purpose  of  making 
repairs,  warehouse  rent,  reloading  cargo,  outward  expenses,  etc. 

6.  Wages  and  provisions  of  crew  from  the  date  of  bearing  up 
until  ready  for  sea. 


GENERAL    AVERAGE.  281 

542.  Contributory  Interests  and  Values. —  The  ship 
contributes  on  its  full  value  at  the  time  which  is  made  the  basis  of 
contribution. 

The  cargo  contributes  on  its  net  market  value  at  the  port  of 
destination,  less  freight  and  charges  saved. 

The  freight  contributes  on  the  full  amount,  less  -J-  for  the 
wages,  etc.,  of  crew.  In  the  States  of  New  York,  Virginia,  Cali- 
fornia, and  some  others,  £  is  deducted. 

The  underwriters  (Insurance  companies)  contribute  to  the  general  average 
such  a  part  of  the  expense  as  the  insured  value  is  of  the  market  value  of  the 
goods  (4O5).  If,  for  example,  a  cargo  is  insured  for  $10000  and  is  worth  in 
the  market  $12000,  the  underwriters  are  liable  to  pay  £  of  the  general 
average  expense. 

543.  To  give  rise  to  general  average,  it  must  be  shown  that 
there  was  an  imminent  common  danger,  that  the  sacrifice  was 
voluntary  and  necessary,   and  that  the  act  was  prudent    and 
successful. 

544.  An  Average  Adjuster  is  a  person  who  is  familiar  with 
the  general  average  laws  of  the  leading  commercial  nations,  and 
who  adjusts  and  apportions  the  losses  and  expenses  of  a  general 
average. 

The  principal  difficulty  of  an  adjuster  is  to  decide  whether  the  loss  should 
he  made  good  by  a  general  average  or  should  be  made  a  special  charge  (par- 
ticular average)  upon  some  particular  interest.  After  the  general  average 
charges  are  determined,  the  apportionment  of  the  loss  among  the  several  con- 
tributory interests  is  a  simple  arithmetical  problem. 

EXAMPLES. 

545.  1.  The  bark  Liberty  sailed  from  New  York  for  Galves- 
ton  with  the  following  cargo  :  Shipped  by  A,  $5600  ;  by  B,  $8700; 
by  C,  $16308  ;  by  D,  $8360.     After  two  days  out  the  bark  en- 
countered heavy  gales  and  was  damaged  to  the  amount  of  $630.14. 
On  the  fifth  day  the  vessel  began  to  take  water,  and  for  the  safety 
of  the  vessel  and  the  cargo  the  bark  bore  away  for  New  York  for 
repairs.    The  disbursements  of  the  agent  at  New  York  were  as  fol- 
lows :  Custom-house  fees,  pilotage,  protest,  towage,  unloading  and 
reloading  cargo,  wharfage,  inspection,  consul  fees,  $1369.43;  bill 
of  H.  Robin  &  Co.,  shipwrights,  etc.,  $436  ;  bill  of  Joseph  Patti, 
ceiling  ship  $194.14,    Agent's  commission  for  advancing  funds 


282 


GENERAL    AVERAGE. 


and  paying  above  bills,  §% ;  on  value  of  cargo  landed^  $17388, 
Wages  and  provisions  of  seamen  from  point  of  deviation,  $630.47. 
The  gross  freight  was  $8096,  and  seamen's  wages,  etc.,  £  of  gross 
freight.  How  is  the  settlement  to  be  made,  the  value  of  the 
ship  being  $10000  and  the  adjuster's  fee  $100  ? 

NOTE. — In  a  general  average,  extracts  from  the  log  of  the  ship,  the  testi- 
mony of  its  officers,  a  complete  statement  of  all  expenses  incurred,  with  the 
vouchers  for  the  same,  and  all  papers  having  any  bearing  upon  the  case  are 
presented  to  the  adjuster.  The  total  amount  of  each  item  is  entered  in  a 
column  at  the  left  of  his  statement  of  charges,  and  the  amount  is  also  entered 
in  its  proper  column  at  the  right.  In  addition  to  the  general  average  column, 
there  are  usually  columns  at  the  right  for  the  special  charges  upon  the  ship, 
owners,  or  cargo. 

STATEMENT  OF  CHAKGES. 


General 

Ship  and 

Total. 

Average. 

Owners. 

1369 

43 

Expense  of  entering  harbor,  landing  cargo,  etc. 

1369 

43 

436 

Bill  of  H.  Robin  &  Co.,  shipwrights,  etc. 

436 

194 

14 

"     "  Joseph  Patti,  ceiling  ship. 

194 

14 

Agent's  commission  for  advancing  funds  and 

99 

98 

paying  above  bills,  5  %  . 

** 

*# 

** 

#:> 

Agent's  commission  on  value  of  cargo  landed, 

#** 

## 

$17388,  \\%. 

•*## 

*# 

630 

47    Wages,  etc.,  of  seamen. 

630 

47 

100 

Adjuster's  fee. 

100 

General  average. 

**## 

#-:f 

3047 

:>?                         Ship  and  owners. 

•**# 

-:;••« 

CONTRIBUTORY  INTERESTS  AND  APPORTIONMENTS  IN  GENERAL 

AVERAGE. 


Ship,  value  10000  @  .***  pays 

#«# 

Freight,  8096 
Less^  4048   4048  @  .***   " 

#*-::- 

*:.'• 

Cargo, 

A,   5600       @  .***   " 

*** 

B,   8700       @  .***   " 

TT*^ 

** 

0,   16308       ©  .***   " 

**# 

** 

D,   8360       @  .***   f< 

*## 

** 

38968  @  .***   " 

##*# 

*-* 

*****  ©  .***   " 



__. 

###•?:- 

** 

GENERAL  AVERAGE. 
SETTLEMENT. 


283 


BALANCES. 

DB 

CB 

To  pay. 

To  receive. 

Vessel  and  Owners. 

Pay  ship's  proportion  of  Gen.  Aver. 

**# 

"  freight's        "               " 

*** 

## 

"  owner's  column. 

*** 

** 

Receive  seamen's  wages. 

### 

vr* 

663 

34 

Cargo. 

Pay  proportion  of  Gen.  Average. 

**** 

** 

1753 

56 

Agents  of  Vessel. 

Receive  their  disbursements. 

**** 

#* 

"            4<    commission. 

#*# 

** 

2316 

90 

Adjusters. 

Receive  their  fee. 

*** 

100 

3047 

37 

3047 

37 

2416 

90 

2416 

90 

2.  The  general  average  charges  were  $4375.86,  and  the  con- 
tributory interests  $64325.  What  was  the  per  cent,  of  loss  ? 
What  was  the  loss  of  Mr.  B.,  whose  goods  were  valued  at  $7250  ? 

S.  Suppose  A's  goods  in  Ex.  1  were  insured  for  $5000,  how 
much  of  the  loss  would  be  shared  by  the  insurance  company  ? 

4.  The  ship  Amazon,  from  Aspinwall  to  New  York,  being  in 
distress,  threw  overboard  part  of  the  cargo,  cut  away  the  masts, 
and  finally  bore  away  to  a  port  of  refuge  to  repair  in  order  to  com- 
plete the  voyage.     The  cost  of.  replacing  masts  and  rigging  cut 
away  was  $6000  (less  -J-  new  for  old);   the  cargo  jettisoned  was 
worth  compared  with  sound  cargo  delivered  at  destination  $2000  ; 
freight  on  cargo  jettisoned,  $200 ;   expenses  of  entering  port  of 
refuge,  discharging,  storing  and  reloading  cargo,  $1000;  wages  of 
master  and  crew  from  time  of  bearing  away  until  ready  for  sea, 
$600  ;  provisions  of  master  and  crew  for  same  time,  $500 ;  adjuster's 
fee,  $100.     The  vessel  was  valued  at  destination  a,t  $20000  (deduct 
gross  repairs  and  add  amount  made  good)  ;  cargo,  value  on  arrival, 
$40000  (add  amount  made  good)  ;   freight  collected,  $4000  (add 
amount  made  good  and  deduct  £).     What  was  the  per  cent,  of 
loss,  and  how  was  the  settlement  made  ? 

5.  The  cargo  of  the  ship  Amazon  was  insured  for  $36000.    How 
much  was  the  claim  against  the  insurance  company  ? 


284:  GENERAL    AVERAGE. 

6.  The  ship  Union,  in  her  passage  from  Liverpool  to  Boston, 
during  a  storm  threw  overboard  cargo  to  the  amount  of  $1580, 
and  cut  away  masts  and  rigging.     She  then  entered  the  port  of 
Halifax  for  repairs.     The  cost  of  replacing  the  masts  and  rigging 
which  were  voluntarily  sacrificed,  was  $4578  (less  £  new  for  old)  ; 
cost  of  repairing  accidental  damage,  $568  ;  freight  on  cargo  jetti- 
soned, $314.75  ;  expense  of  entering  port  of  refuge,  discharging 
cargo,  etc.,  $716.87 ;  wages  and  provisions  of  crew,  $608 ;  adjuster's 
fee,  $150.     The  value  of  vessel  on  arrival  at  Boston  was  $30000 
(deduct  gross  repairs  and  add  amount  made  good) ;  value  of  cargo 
delivered,  less  freight  and  duty,  $48475  (add  amount  jettisoned)  ; 
total  expected  earning  of  freight,  $16320  (less  -J  in  Boston.     See 
Art.  54:2.).     The  cargo  was  shipped  by  the  following  persons : 
A  $8519,  B  $20376,  C  $6875,  and  D  $14285.    The  cargo  jettisoned 
was  a  part  of  A's  shipment.     How  ought  the  settlement  to  be 
made? 

7.  The  ship  Ocean  Queen,  from  Pernambuco  to  New  York, 
sprang  a  leak  off  Cape  St.  Roque,  and  for  the  safety  of  the  vessel 
and  cargo,  threw  overboard  part  of  the  cargo  and  put  into  Maran- 
ham  for  repairs.     The  disbursements  at  Maranham  by  the  master 
of  the  vessel,  including  commissions,  were  as  follows  :  Expenses  of 
entering  harbor,  discharging,  storing,  and  reloading  cargo,  $648.75 ; 
caulking  and  painting  ship,  carpenter  work,  etc.,  $843.    Value  of 
cargo  delivered  at  New  York,  $34310.24 ;    of  cargo  jettisoned, 
$1580.76  ;  freight  on  cargo  jettisoned,  $364  ;  wages  and  provisions 
of  crew,  $304 ;  adjuster's  fee,  $150 ;  agent's  commission  for  col- 
lecting amount  in  general  average,  %\%.     How  shall  the  settle- 
ment be  made,  if  the  net  value  of  the  ship  was  $3157  (value  on 
arrival  $4000,  less  repairs  $843),  and  the  total  expected  earning 
of  freight  was  $2516  (less  £)  ? 

8.  A  vessel  which  put  into  a  port  of  refuge  for  repairs  was 
without  funds.     It  being  very  difficult  to  obtain  a  loan  on  bot- 
tomry, or  to  negotiate  a  draft  on  the  owners  of  the  vessel,  the  mas- 
ter was  obliged  to  sell  part  of  the  cargo  to  raise  funds.    Value  of 
cargo  sold  compared  with  cargo  delivered  at  destination,  $4566.06 ; 
produced  at  sale,  $2985.30  ;  freight  on  cargo  sold  compared  with 
freight  on  cargo  delivered,  $363.93.     What  was  the  cost  of  funds, 
and  how  much  should  be  apportioned  to  each  interest,  the  general 
average  charges  being  $773.52,  the  special  charges  on  ship  $956.10, 
and  on  the  owners  $1181.06  ? 


CLEARING     HOUSES. 


DEFINITIONS. 

546.  A  Clearing  House  is  a  place  where  the  daily  exchanges 
are  effected  between  banks,  and  where  the  payments  of  the  bal- 
ances resulting  from  such  exchanges  are  made. 

The  New  York  Clearing  House  was  the  first  of  the  kind  established  in 
America,  and  began  its  operations  Oct.  11,  1853.  Since  that  time  Clearing 
Houses  have  been  established  in  all  the  principal  cities  of  the  country,  there 
now  being  twenty-two  in  the  United  States. 

Before  the  Clearing  House  at  New  York  was  established  it  was  necessary 
for  each  bank  every  morning  to  make  up  its  accounts  with  every  other  bank, 
and  to  send  a  messenger  to  the  debtor  banks  to  present  accounts  and  receive 
balances,  which  were  adjusted  in  gold.  This  finally  became  so  laborious, 
dangerous,  and  complicated,  that  balances  were  arranged  weekly  every  Friday. 
The  Clearing  House  obviated  this.  Its  settlements  are  made  so  rapidly  that 
the  transactions  adjusted  through  it  have  amounted  in  a  single  day  to  over 
$250,000,000— all  settled  within  an  hour. 

The  establishment  of  the  Clearing  House  closed  2500  bank  ledger  accounts, 
with  numerous  daily  entries  in  each,  and  enabled  the  banks  to  settle  with  each 
other  every  day  without  loss  or  delay,  and  with  comparatively  little  trouble. 

547.  The  New  York  Clearing  House  Association  is 
composed  of  45  national  and  12  State  banks,  and  the  assistant 
treasurer  of  the  United  States  at  New  York.      The  remaining 
banks  (4  national  and  9  State)  make  their  exchanges  through  the 
others. 

During  the  year  ended  October  1,  1881,  the  total  exchanges  were  more 
than  $48,000,000,000,  while  the  balances  paid  in  money  were  less  than 
$1,800,000,000.  The  average  daily  balances  paid  were  nearly  $6,000,000,  or 
about  §\%  of  the  amount  of  the  settlements.  The  balances  paid  in  money 
during  the  year  consisted  of  $1,394,966,000  in  clearing  house  certificates  of  the 
Bank  of  America  (548,  15),  legal-tenders  (189)  amounting  to  $8,633,161, 
and  $372,419,000  in  gold  coin,  weighing  686£  tons.  The  largest  transactions 
for  any  one  day  were  on  the  28th  of  November,  1880,  and  amounted  to 
$295,821,422.37. 


286  CLEARING    HOUSES. 

548.  The  Daily  Routine  at  the  New  York  Clearing  House 
is  as  follows : 

1.  The  checks,  drafts,  etc.,  which  make  up  the  exchange  of  each  bank 
are  those  which  were  received  the  previous  day  on  deposit,  in  payment  of 
notes  and  drafts,  and  by  mail  from  the  correspondents  of  the  bank.     The 
checks  which  are  received  by  the  early  morning  mail  are  added  to  the  above 
on  the  morning  of  the  exchange.     Each  bank  enters  on  slips  of  paper  (See 
Form  1),  a  list  of  the  checks,  drafts,  etc.,  upon  each  of  the  other  banks.     The 
slips  together  with  the  checks  are  enclosed  in  sealed  envelopes  or  packets, 
upon  the  back  of  which  is  printed  the  name  of  the  bank  owning  the  checks 
and  the  name  of  the  bank  upon  whom  the  checks  are  drawn.     The  total 
amount  is  written  upon  the  outside  of  the  envelopes.     These  amounts  are 
entered  upon  the  "  Settling  Clerk's  Statement  "  (Form  4)  under  the  head  of 
"  Banks  Dr."  opposite  the  names  of  the  respective  banks,  and  the  aggregate 
is  found. 

These  amounts  are  also  entered  upon  small  tickets  the  use  of  which  will 
be  explained  hereafter.  The  messenger's  "Receipt  List"  (548,7)  is  also 
prepared  at  the  bank. 

2.  Each  bank  sends  to  the  Clearing  House  a  messenger  and  a  Settling 
Clerk,  the  former  to  deliver  the  packets  of  checks,  drafts,  etc.,  of  which  his 
exchange  is  composed,  and  the  latter  to  receive  the  checks,  etc.,  against  his 
bank  from  the  messengers  of  the  other  banks. 

8.  Each  settling  clerk,  as  he  enters  the  Clearing  House,  leaves  at  the 
desk  of  the  assistant  manager  a  "credit  ticket"  (Form  3),  showing  the  total 
amount  of  the  exchanges  which  he  brings  to  the  Clearing  House  against  the 
other  banks.  For  example,  the  clerk  from  the  Bank  of  America  leaves  the 
following : 

(Form  1.) 


J\'o.  6.  fy-ril  5, 

Neto  fork  Clearing  ©onsc. 
Credit  BANK  OF  AMERICA,  $3,416,728.37. 

G.  H.    WATSON,  JR.,  Settling-  Clerk. 


4.  The  amounts  on  these  tickets  are  entered  on  the  "Clearing  House 
Proof"  (See  Form  7),  under  the  head  of  "  Banks  Cr."  and  added  together, 
making  in  tlje  example  $25,416,328.96.  This  is  the  total  sum  sent  in  by  all 
the  banks,  and  is  called  the  Credit  Exchange.  Since  each  packet  is  taken 
away  by  some  bank,  the  total  of  the  amounts  entered  under  the  head  of 
"  Banks  Dr. ,"  after  the  exchange  is  made,  should  agree  with  the  total  under 
the  head  of  "  Banks  Cr." 


CLEARING    HOUSES.  287 

5.  Promptly  at  10  o'clock,  the  assistant  manager  strikes  a  bell  and  says 
"  Take  your  places  " — "  Order  "— "  Ready,  go."     A  fine  is  imposed  upon  those 
who  are  not  in  their  places  at  the  first  ringing  of  the  bell. 

6.  Each  Settling  Clerk  is  now  at  his  desk  and  has  before  him  the  "  Settling 
Clerk's  Statement "  (See  Form  4),  the  debit  side  of  which  shows  the  amount  of 
checks,  etc.,  his  bank  has  against  each  of  the  other  banks.    The  credit  side,  on 
which  is  entered  the  amounts  received  from  the  other  banks,  is  now  blank. 

7.  The  messengers  stand  opposite  their  respective  desks,  and  have  the 
packets  arranged  in  an  open  box  in  the  order  of  their  delivery.     Thus,  the 
messenger  of  No.  6  has  his  packets  in  the  following  order  :  5,  4,  3,  2, 1,  76,  75, 
74,  72,  etc.     He  also  has  a  "  Receipt  List,"  which  is  a  copy  of  the  "  Banks  Dr." 
of  the  "  Settling  Clerk's  Statement  "  with  a  blank  column  for  the  signatures 
of  the  clerks  of  the  receiving  banks. 

8.  At  the  second  ringing  of  the  bell,  each  messenger  advances  one  step  for- 
ward and  is  brought  opposite  the  first  desk  at  which  his  delivery  is  to  be 
made.     He  delivers  the  packet  of  checks  designed  for  it,  and  also  the  "  Receipt 
List."     The  Settling  Clerk  compares  the  amount  on  the  packet  with  the 
amount  on  the  list,  and,  if  correct,  signs  his  initials  opposite  the  amount, 
and  returns  the  list  to  the  messenger.     He  also  enters  the  amount  received 
on  his  statement  opposite  the  name  of  the  bank  under  the  head  of  "  Banks 
Cr.,"   before  receiving  another  packet.      The   messenger  goes  through  the 
delivery  at  each  desk  in  like  manner.     The  whole  line  of  messengers  advance 
at  the  same  time,  and  each  messenger  performs  a  similar  operation. 

In  10  or  15  minutes  the  circuit  of  the  58  desks  is  made,  bringing  each 
messenger  to  the  starting  point  opposite  his  own  desk.  His  "Receipt  List," 
signed  by  every  Settling  Clerk,  is  the  voucher  to  his  bank  that  he  has  deliv- 
ered all  the  checks  intrusted  to  his  care. 

9.  Each  Settling  Clerk  has  now  on  his  desk  the  packets  of  checks  which 
constitute  his  Debit  Exchange.     He  has  already  entered  the  amounts  in  his 
Statement  under  the  head  of  "  Banks  Cr." 

As  soon  as  the  exchange  is  made  each  messenger  returns  to  his  bank  with 
the  packets  of  checks,  and  with  a  memorandum  of  the  total  debit  exchange 
which  has  been  furnished  to  him  by  the  Settling  Clerk,  and  the  balance  in 
favor  of  or  against  the  bank.  The  Settling  Clerks  are  obliged  to  remain  until 
the  assistant  manager  announces  an  exact  proof. 

The  messengers  call  back  the  amounts  on  the  packets  as  they  place  them 
in  their  satchels  preparatory  to  returning  to  their  respective  banks. 

10.  The  Settling  Clerks  carefully  revise  the  addition  of  the  column  "  Banks 
Cr.,"  and  send  to  the  desk  of  the  assistant  manager  a  "Balance  Ticket," 
which  shows  the  amount  brought,  the  amount  received,  and  the  balance  for 
or  against  the  bank.     (See  Form  2.) 

The  amounts  received  are  entered  on  the  Clearing  House  Proof  under  the 
head  of  "Banks  Dr.,"  and  the  balances  in  the  proper  columns.  The  sum  of 
the  amounts  under  the  head  of  "Banks  Dr."  should  equal  the  sum  under 
"  Banks  Cr."  (See  548,  4.) 


288  CLEARING    HOUSES. 

(Form  2.) 


JVb.  6.  jlpril  5,  IS $2. 

Neto  JDork  (Clearing  Ijouss. 

(Debit  BANK  OF  AMERICA,  Amount  reo'd,    $8,581,309.78. 
Credit       «         "  "  «   brought,    $3.416,728.37. 

$164, 5 &1--43-,  debit  balance  due  Clearing  House. 
Cr.  bal.  due  BANK   OF  AMERICA,  $  ___ 

(7.  JZ".    TF^TSO.V,  JR.,  Settling-  Clerk. 


11.  When  the  exchange  was  made,  each  messenger  distributed  a  set  of 
tickets  (Form  3)  on  which  were  amounts  corresponding  with  the  amounts  on 
the  packets  of  checks.     These  tickets  are  compared  with  the  amounts  on  the 
Settling  Clerk's  Statements  under  the  head  of  "Banks  Cr.,"  and  ought  to 
correct  all  errors  of  transcription  although  the  checks  have  been  taken  away. 

(Form  3.)  No.  8. 

NATIONAL    CITY    BANK. 

From  No.  6, 

BANK     OF     AMERICA. 

$876,439.43. 

12.  The  assistant  manager  announces  the  error  in  the  proof  at  10:45  or 
earlier.     The  Settling  Clerks  have  in  the  meantime  been  revising  their  work. 
When  errors  are  discovered  new  balance  tickets  are  sent  to  the  assistant 
manager's  desk  with  the  amount  of  the  error  entered  therein.     To  correct 
errors  in  addition,  the  Settling  Clerk's  Statements  are  all  passed  to  the  right 
and  added  by  another  clerk.      If  the  error  is  not  then  discovered,  clerk  of 
Bank  No.  1  passes  down  the  line  with  his  statement  and  calls  back  the  amount 
he  has  received  from  each  bank.     The  second  clerk  immediately  follows  the 
first,  and  the  third  the  second  and  so  on.     At  the  other  end  of  the  line  the 
same  operation  takes  place,  No.  76  passes  down  the  line,  followed  by  No.  75, 
etc.     This  is  the  final  method  of  revision,  and,  if  the  additions  are  correct, 
should  correct  all  errors. 

13.  There  is  a  scale  of  fines  for  all  errors  discovered  after  10:45.     For  all 
errors  remaining  undiscovered  after  11:15,  the  fine  is  doubled ;  after  12,  the 
fine  is  quadrupled. 

14.  All  balances  due  the  Clearing  House  are  paid  before  \\  o'clock,  p.  M., 
and  the  creditor  banks  send  for  the  amounts  due  them  between  1^  and  2  o'clock. 


CLEARING    HOUSES. 


289 


15.  To  save  the  risk  and  inconvenience  of  handling  gold,  settlements  are 
made  by  gold  Clearing  House  Certificates  of  the  Bank  of  America,  the  com- 
mon coin  depository  of  the  Associated  Banks.     These  certificates  are  valid 
only  in  the  Clearing  House   settlements,  or  directly  between  the  bunks. 
Balances  less  than  $1000  are  paid  in  gold  or  legal-tenders  (188). 

16.  Errors  in  exchanges,  and  claims  arising  from  the  return  of  checks,  or 
from  any  other  cause,  are  adjusted  directly  between  the  banks  who  are  parties 
to  them,  and  not  through  the  Clearing  House. 

(Form  4.)* 
No.  6.  BANK    OF    AMERICA. 

SETTLING  CLERK'S  STATEMENT,  April  5,  1882. 


No. 

Banks. 

Banks  Dr. 

Banks  Cr. 

No. 

1 

B'k  of  N.  Y.  Nat'l  Bk'g  Ass'n, 

362 

189 

76 

426 

134 

42 

1 

2 

Manhattan  Company, 

228 

065 

43 

280 

772 

87 

2 

3 

Merchants'  National  Bank, 

756 

784 

80 

652 

668 

16 

3 

4 

Mechanics'  National  Bank, 

275 

238 

92 

438 

591 

34 

4 

5 

Union  National  Bank, 

537 

564 

27 

377 

418 

72 

5 

7 

Phenix  National  Bank, 

142 

728 

11 

344 

836 

19 

r< 
i 

8 

National  City  Bank, 

876 

439 

42 

615 

971 

24 

8 

10 

Tradesmen's  National  Bank, 

169 

235 

08 

313 

185 

50 

10 

11 

Fulton  National  Bank, 

68 

482 

58 

131 

731 

34 

11 

Exchanges, 

3416 

728 

37 

3581 

309 

78 

Balance, 

164 

581 

41 

. 

(Form  5.) 
NEW  YORK  CLEARING  HOUSE  PROOF,  April  5,  1882. 


-J 

Banks. 

Du«  Clearing 
House. 

Banks.     Dr. 

Banks.     Cr. 

Due  Banks. 

No. 

1 

B'k  of  N.  Y.  Nat'l  Bk'g  Ass'n, 

153 

161 

54 

2 

417 

853 

21 

2 

734 

415 

38 

316 

562 

17 

1 

2 

Manhattan  Company, 

3 

670 

729 

36 

3 

517 

567 

82 

2 

8 

Merchants'  National  Bank, 

4 

189 

437 

29 

4 

484 

123 

49 

294 

686 

20 

3 

4 

Mechanics'  National  Bank, 

2 

234 

163 

46 

2 

425 

876 

50 

191 

713 

04 

4 

5 

Union  National  Bank, 

301 

190 

94 

2874 

109 

28 

2 

572 

918 

34 

5 

6 

Bank  of  America, 

164 

581 

41 

3581 

309 

78 

3 

416 

728 

37 

6 

7 

Phenix  National  Bank, 

245 

R85 

43 

2537 

41  S 

4-2 

2 

291 

532 

99 

7 

8 

National  City  Bank, 

176 

895 

20 

704 

333 

50 

1 

5871438 

30 

8 

10 

Tradesmen's  National  Bank, 

1 

437 

528 

49 

1 

573 

419 

22 

135 

890 

73 

10 

11 

Fulton  National  Bank, 

709 

446 

17 

312308 

55 

102 

862 

38 

11 

1041 

714 

52 

25 

416 

328 

96 

25 

416  328  96 

1041 

714 

52 

*  For  economy  of  space,  Forms  4  and  5  are  given  with  only  10  banks. 


DETECTION     OF    ERRORS 


TRIAL    BALANCES. 

549.  The  following  hints  apply  to  the  detection  of  errors  in 
trial  balances,  or  in  any  operation  in  which  errors  are  made  in 
addition  or  subtraction,  or  in  transferring  numbers  from  one  place 
to  another. 

1.  Ascertain  the  exact  amount  of  the  error.     Much  time  is 
sometimes  wasted  in  looking  for  errors  which  do  not  actually  exist. 

2.  Revise  carefully  the  additions  of  the  trial  balance  before 
looking  for  the  error  in  the  ledger  or  other  books. 

3.  If  the  error  is  in  one  figure  only  (as  2000,  100,  50,  etc.),  it 
is  probably  an  error  in  addition  or  subtraction. 

4.  If  an  amount  is  entered  on  the  wrong  side  of  an  account,  or 
is  added  when  it  should  be  subtracted  or  vice  versa,  the  error  will 
be  twice  the  amount. 

5.  If  the  digits  of  any  number  are  written  to  the  right  or  left 
one,  two,  or  three  places,  and  the  error  be  divided  by  9,  99,  or 
999  respectively,  the  quotient  will  be  the  number. 

Thus,  if  $427  be  written  $4.27,  the  error  will  be  $422.73  ;  which  divided 
by  90  (by  9  and  11),  the  quotient  will  be  $4.27. 

The  number  of  9's  by  which  the  number  can  be  exactly  divided  is  equal 
to  the  number  of  places  which  the  number  has  been  transferred  to  the  right 
or  the  left. 

6.  If  two  consecutive  digits  of  any  number  are  transposed,  the 
error  will  be  a  multiple  of  nine  ;  and  the  quotient  obtained  by 
dividing  the  error  by  9  will  express  the  difference  between  the 
digits  transposed. 

Thus,  if  437,  be  written  473,  the  error  will  be  36 ;  which  divided  by  9 
produces  4,  the  difference  between  3  and  7.  The  same  error,  36,  will  arise  if 
the  figures  transposed  are  0  and  4,  1  and  5,  2  and  6,  4  and  8,  or  5  and  9. 

7.  If  the  error  contains  a  number  of  figures,  it  is  probable 
that  some  account  or  item  has  been  omitted. 

8.  Look  for  the  error  systematically,  and  not  in  certain  por- 
tions of  the  work  selected  at  random. 


MISCELLANEOUS    EXAMPLES.* 

55O.  1.  Add  17£,  28},  36J,  44£,  89T%,  and  76£ ;  multiply  the 
sum  by  87  ;  subtract  1022JJ  from  the  product ;  and  divide  the 
remainder  by  234f. 

2.  Divide  eighty-three,  and  seventy-five  hundredths  by  one  hun- 
dred and  twenty-five  ten-thousandths ;  add  to  the  quotient  sixty- 
eight,  and  six  hundred  and  twenty-five  thousandths  ;  and  multiply 
the  sum  by  three,  and  two-tenths. 

3.  How  many  minutes  in  the  month  of  February,  1900  ? 

4.  Find  the  cost  of  7312  pounds  of  meal  at  $2.25  per  cwt. 

5.  The  difference  in  the  local  time  of  two  places  is  1  lir.  7  min. 
13  sec.  ;  what  is  the  difference  in  longitude  ? 

6.  Find  the  number  of  square  yards  of  paving  in  a  street, 
3000  ft.  long  and  50ft.  wide. 

7.  What   is   the   charge  for  packing,  marking,  and  shipping 
251  bales  merchandise  at  5s.  6d.  per  bale  ? 

8.  If  46  T.  12  cwt.  of  coal  are  worth  $174.75,  what  is  the  value 
of  37  T.  8  cwt.  ? 

9.  How  many  square  yards  of  linoleum  would   cover  a  floor 
22  ft.  6  in.  by  15//.  4  in.  ?     Find  its  value  at  63^  per  sq.  yd. 

10.  What  is  the  freight  of  5  T.  9  cwt.  2  qr.  8  ?£.,  at  70  shillings 
per  ton  (2240  Ibs.)  ? 

11.  Find  the  cost  of  4  T.  7  cwt.  3  qr.  20  Ib.  of  iron,  at  £15  4s. 
Qd.  per  ton  (2240  Ibs.). 

12.  What  is  the  weight  in  grams  of  the  U.  S.  gold  dollar  ? 

13.  What  is  the  value  of  a  Lac  (100,000)  of  rupees  in  U.  S. 
money  ?     (See  Art.  192,  India.) 

14.  A  bank  collected  a  draft  of  $9375.16.     What  were  the 
proceeds,  the  charge  for  collection  being  \%  ? 

15.  What  is  the  cost  of  insuring  $18000  at  750  per  $100  ? 

16.  What  is  the  cost  of  250  ft,  3-ply  hose,  at  60  cts.  per  foot, 
less  30  and  10$,  and  5  sets  couplings  at  $1.50  each  ? 

17.  What  is  ty%  of  £159  13s.  lOd. 

18.  A's  property  is  assessed  at  $7500,  and  the  rate  of  taxation 
is  $2.165  on  $100.      What   is  his   tax,  including  a  commission 
of  \%  ? 

*  Answers  omitted. 


292  MISCELLANEOUS    EXAMPLES. 

19.  What  is  the  duty  at  60%  on  an  invoice  of  silk  amounting  to 
36475  francs  ? 

20.  A  merchant  buys  a  bill  of  dry  goods,  Apr.  16,  amounting 
to  $6,377.84,  on  the  following  terms:    4  months,  or  less  5%  30 
days.     How  much  would  settle  the  account  May  16  ?    The  above 
discount  is  equivalent  to  what  rate  per  cent  per  annum  ? 

21.  Mr.  B.  purchased  36150  pounds  of  hay  at  $16.50  per  ton, 
and  16438  pounds  of  oats  at  70  cents  per  bushel.     He  sold  the 
hay  at  a  gain  of  16%,  and  the  oats  at  a  loss  of  8%.     What  were 
the  proceeds  ? 

22.  A  merchant  buys  goods  at  a  discount  of  40  and  20%  from 
the  list  price,  and  sells  at  a  discount  of  30  and  10%.     What  is  the 
gain  per  cent  ? 

28.  Mar.  16,  a  merchant  buys  a  bill  of  goods  amounting  to 
$2475  on  the  following  terms  :  4  months,  or  less  5%  if  paid  in 
30  days.  Apr.  15  he  makes  a  payment  of  $1000,  with  the  under- 
standing that  he  is  to  have  the  benefit  of  the  discount  of  5%. 
With  what  amount  should  he  be  credited  on  the  books  of  the 
seller?  How  much  would  be  due  July  16,  the  expiration  of  the 
4  months  ? 

24.  May  10,  A  buys  a  bill  of  goods  amounting  to  $5000  on 
the  following  terms :  60  days,  or  1%  discount  in  30  days,  or  2% 
discount  in  10  days.     May  20  he  makes  a  payment  of  $2000,  and 
June  9,  of  $2500.     How  much  would  be  due  July  9,  the  end  of 
the  60  days'  credit  ? 

25.  Oct.  16,  B  bought  a  bill'  of  merchandise  amounting  to 
$2000   on   the   following   terms  :    4   months,  or   5%  discount  in 
30  days,  or  6%  discount  in  10  days.     Oct.  26  he  made  a  payment 
of  $1000.     How  much  would  settle  the  bill  Nov.  15  ? 

26.  B  bought  a  bill  of  merchandise  May  16  amounting  to 
$3416.72  on  the  following  terms :   4  w?ox.,  or  less  5%  30  days.     He 
paid  on  account  June  21   (6  days  after  the   expiration   of  the 
30  days)  $3000,  with  the  understanding  that  he  should  have  the 
benefit  of  the  discount  by  paying  interest  for  the  time  elapsed, 
at  6%  per  annum.     How  much  was  due  Sept.  16,  no  compound 
interest  being  reckoned  ? 

27.  Paid  for  transportation  $664.95  on  an   invoice  of  goods 
amounting  to  $8866.     What  per  cent,  was  the  value  of  the  goods 
thereby  increased  ?     What  per  cent,  must  be  added  to  the  invoice 
cost  to  make  a  profit  of  20^  on  the  full  cost  ? 


MISCELLANEOUS    EXAMPLES.  293 

28.  Find  the  total  freight  on  68  ft.  mdse.  at  35  shillings  per 
ton   (40  cu.  ft.),   and   123  ft.  at  40  shillings  per  ton,  plus   10% 
primage  on  each  item. 

29.  A  merchant  buys  a  bill  of  goods  amounting  to  $1000  on  a 
credit  of  four  months,  or  6%  off  for  cash.     He  pays  $500  cash. 
For  what  amount  should  his  account  be  credited  ? 

30.  Bought  coal  by  the  long  ton  at  $3.64,  and  sold  by  the 
short  ton  at  $4.25.     What  was  the  gain  per  cent  ? 

31.  A  bought  a  bill  of  merchandise  July  24,  1879,  amounting 
to  $6287.45  on  the  following  terms :  6  months,  or  less  4%  30  days. 
He  paid  on  account  Aug.  23,  1879,  $5000,  with  the  understand- 
ing that  the  payment  would  cancel  an  equitable  amount  of  the 
bill.     How  much  was  due  Jan.  24,  1880  ? 

82.  A  commission  merchant  in  Chicago  sells  for  me  12  bales 
brown  sheeting,  each  bale  containing  800  yards,  at  7  cts.  per 
yard ;  pays  transportation  and  other  charges  amounting  to  $72 ; 
and  invests  the  proceeds  in  flour  at  $4.80  per  barrel.  If  he  charges 
%%%  for  selling  and  \\%  for  purchasing,  how  many  barrels  of  flour 
does  he  send  me  ? 

33.  Find  the  date  of  maturity  and  the  net  proceeds  of  a  note 
for  $5000,  dated  May  16,  payable  4  months  after  date,  and  dis- 
counted July  21  at  6%. 

34.  When  the  above  note  became  due,  its  maker  had  discount- 
ed at  6%  a  new  note,  payable  90  days  after  date,  whose  proceeds 
were  sufficient  to  pay  the  first  note.     What  was  the  face  of  the 
new  note  ? 

35.  Apr.  1,  a  merchant  buys  a  quantity  of  coffee  on  90  days' 
credit,  with  privilege  of  discounting  within  30  days  from  date  of 
purchase  at  the  rate  of  Q%  per  annum  for  the  unexpired  time. 
Apr.  16  he  makes  a  payment  of  $28000  on  account,  no  actual 
invoice  having  been   rendered.     May  1   he  receives  the  invoice, 
amounting  to  $29215,  and  on  the  same  date  full  settlement  is 
made.     What  amount  was  required  to  cancel  the  bill  ?     (Exact 
days,  360  days  to  the  year.) 

36.  Divide  $2000  in  such  a  manner  between  two  brothers, 
aged  16  and  19  years  respectively,  so  that  when  they  arrive  at 
21  years  of  age  they  will  have  equal  amounts,  money  being  worth 
6%  simple  interest. 

87.  What  would  be  the  share  of  each  if  money  is  worth  6% 
compound  interest  ? 


294  MISCELLANEOUS    EXAMPLES. 

38.  Find  the  amount  due  on  the  following  note  Jan.  1,  1883, 
by  the  United  States  and  the  Mercantile  Rules  : 


$50QOT°(fe-  DAVENPORT,  IOWA,  May  1,  1878. 

On  demand,  I  promise  to  pay  EDWIN  D.  MORGAN,  or  order, 
Five  thousand  dollars,  with  interest  at  ten  per  cent.,  for  value 
received.  E.  H.  CONGER. 

On  this  note  the  following  payments  were  indorsed  : 

Received  Jan.  16,  1879,  $400.        Received  Dec.  12,  1880,  $150. 

Received  Sept.  7,  1879,  $100.        Received  Aug.  18,  1881,  $850. 

Received  May    1,  1880,  $500.        Received  Apr.  23,  1882,  $100. 

39.  How  much  would  have  been  due  on  the  above  note  if  no 
rate  of  interest  had  been  mentioned  in  the  note  ? 

40.  What  is  the  value  of  a  draft  on  Hamburg  of  17468  marks 
at  95| ? 

41.  C.   of  London   owes   me  for  goods  sold  on  my  account, 
£129  18s.  7d.     How  much  do  I  receive  in  payment,  if  I  draw  a 
bill  of  exchange  for  the  amount  and  sell  it  at  4.85-f? 

42.  My  agent  in  Paris  buys  an  invoice  of  merchandise  amount- 
ing to  12488  francs,  at  a  commission  of  %\%.     What  is  the  cost 
of  the  draft  which  I  remit  in  payment,  the  rate  of  exchange  being 
5.17|? 

43.  An  exporter  sold  the  following  bills  oi  exchange  through 
a  broker:  10000  francs  on  Paris  at  5.16|,  £375  16s.  8d.  on  Lon- 
don at  4.83£,  16480  marks  on  Hamburg  at  94-|,  5287  guilders  on 
Amsterdam  at  41-J.     What  were  the  proceeds,  brokerage  \%  ? 

44-  A  commission  merchant  at  New  York  sells  goods  for  A.  of 
Havre  to  the  amount  of  $3435.27,  and  charges  a  commission  of 
*ty%  for  selling.  What  is  the  face  of  the  draft  which  he  purchases 
and  remits  in  settlement,  exchange  being  5.27  ? 

45.  My  agent  in  London  has  purchased  for  me,  at  a  commis- 
sion of  2£$,  375  dozen  kid  gloves  at  496?.  per  dozen,  and  636  yards 
silk  at  9s.  6d.  per  yard.     When  exchange  is  $4.86J,  what  will  be 
the  cost  of  the  draft  which  I  remit  to  him  in  settlement  ? 

46.  Purchased  in  England,  merchandise  amounting  to  £324 
10s.  7^.,  and  paid  freight  and  duties  $487.34.     How  much  per  £ 
must  I  sell  these  goods  to  gain  12£%  on  the  full  cost,  and  what 
must  I  charge  for  an  article  invoiced  at  6s.  8^.,  exchange  4.88  ? 

47.  Bought  stock  at  1.16|  and  sold  at  1.12-J.     Loss,   $1295. 
What  was  the  par  value  of  the  stock  ? 


21ISCELLANEOUS     EXAMPLES. 


295 


48.  Average  the  following  account : 

Mar.  16,  1882,        $874.32  on  30  days      credit. 

"  31,  " 
May  5,  " 

"  21,  " 
June  18,  « 
July  3,  " 

"  24,  " 
Aug.  19,  " 
Sept.  13,  " 

49.  Average  the  following  account.     What  will  be  the  amount 
due  Jan.  1,  1883  ? 


518.65   " 

60     " 

373.78   « 

4  months 

429.31    « 

60  days 

657.70   " 

30    " 

242.28   « 

60     " 

983.75   " 

4  months 

716.30   « 

4        « 

536.60   " 

60  days 

Dr. 


DANIEL  S.  LAMOKT,  Albany,  N.  Y. 


Or. 


1882. 

1882. 

July  16 

Mdse.,  4  mo. 

$876 

14 

Sept.10 

Cash,  .  .  . 

$900 

00 

Aug.  4 

"   60  da. 

415 

65 

"  21 

tt 

700 

00 

Sept.10 

"   30  da. 

797 

38 

Oct.  13 

a 

500 

00 

"  21 

11   30  da. 

686 

96 

"  31 

Mdse.,  30  da. 

322 

16 

Oct.  13 

"    4  mo. 

524 

27 

Nov.  2 

Cash,  .  .  . 

400 

00 

"  31 

"   30  da. 

859 

75 

"  28 

Note,  4  mo. 

800 

00 

Nov.  28 

"   60  da. 

263 

31 

Dec.  27 

Cash,  .  .  . 

500 

00 

Dec.  1 

"   60  da. 

172 

64 

"  30 

"   30  da. 

938 

52 

50.  Prepare  an  account  current,  including  interest  at  6%  to 
Jan.  1,  1883,  from  the  above  ledger  account,  according  to  the  form 
and  method  of  Art.  454. 

51.  Sold  five  $1000  bonds  at  1.16-f,  and  invested  the  proceeds 
in  railroad  stock  at  92-J,  which  I  sold  at  98 J.     "What  was  the  gain 
on  the  stock,  allowing  usual  brokerage  ? 

53.  Sold  Aug.  11,  1879,  500  shares  Chicago  &  Alton,  s.  10,  at 
94£,  and  covered  my  short  sale  Aug.  16,  1879,  at  91.  What  was 
my  profit,  allowing  the  usual  brokerage  ? 

53.  What  annual  income  will  be  obtained  by  investing  $9923.75 
in  bonds,  bearing  5%  interest,  and  purchased  at  1.16}? 

54.  What  is  the  duty  on  a  block  of  marble  2  x  3  x  7  ft.,  im- 
ported from  Italy,  dutiable  value  3450  lire,  and  duty  $1  per  cubic 
foot  and 


APPENDIX. 


DRILL     EXERCISES,    SHORT     METHODS,    ETC. 

551.  Useful  Hints  in  Addition.—  1,  Write  the  numbers 
in  vertical  lines.     Irregularity  in  the  placing  of  figures  is  the 
cause  of  many  errors. 

2.  Think  of  results  and  not  of  the  numbers,  themselves.   Thus, 
in  Ex.  1,  Art.  555,  do  not  say  3  and  4  are  7  and  9  are  16,  etc., 
but  7,  16,  26,  etc. 

3.  Make  combinations  of  10  or  other  numbers  as  often  as  pos- 
sible, and  add  them  as  single  numbers.     When  a  figure  is  repeated 
several  times,  multiply  it  instead  of  adding. 

Add  9  and  1,  8  and  2,  7  and  3,  6  and  4,  5  and  5,  4,  3  and  3,  etc.,  as  10  ;  7 
and  2,  6,  2  and  1,  4  and  5,  etc.,  as  9  ;  2  and  3,  4  and  1,  2,  2  and  1,  as  5  ;  etc.,  etc. 

4.  To  avoid  repeating  the  work,  in  case  of  interruption,  write 
the  figures  to  be  carried  in  pencil  underneath,  as  in  Ex.  4. 

5.  In  adding  long  columns,  prove  the  work  by  adding  each 
column  separately  in  the  opposite  direction,  before  adding  the 
next  column.     If,  by  adding  both  upwards  and  downwards,  the 
two  results  agree,  the  work  is  probably  correct. 

552.  Drill  Exercise  in  Addition.— Take  any  number  less 
than  1000 ;  repeat  the  number ;  add  the  two  numbers  ;  add  the 
three  numbers  ;  add  the  last  three  numbers,  and  so  continue  until 
there  are  twelve  numbers.     The  numbers  expressed  by  the  three 
right  hand  figures  of  the  fourth  and  twelfth  numbers  will  be  the 
same,  if  the  original  number  is  even,  and  will  differ  by  500  if  the 
original  number  is  odd.     Add  all  the  numbers.     The  sum  will 
equal  1104  times  the  original  number.     (See  Ex.  3,  Art.  555.) 

553.  Drill  Exercise  in  Subtraction. — Take  any  number 
less  than  1COO ;   subtract  it  from  1000;   subtract  the  remainder 


DRILL    EXERCISES. 


297 


from  the  last  number,  omitting  the  fourth  figure  and  borrowing 
from  the  fourth  place  when  necessary ;  so  continue  until  sixteen 
subtractions  have  been  made.  The  seventh  and  sixteenth  remain- 
ders will  be  the  same.  Add  the  numbers.  The  three  right-hand 
figures  of  the  sum  will  be  the  same  as  the  three  right-hand  figures 
of  the  product  obtained  by  multiplying  the  original  number  by 
391.  (See  Ex.  4,  Art.  555.) 

554.  Drill  Exercise  in  Multiplication  and  Division. — 
Take  any  number  ;  find  the  continued  product  of  it  and  any  set 
of  numbers.  Use  the  last  product  as  a  dividend,  and  divide  it  by 
the  same  numbers  in  the  same  order,  using  each  quotient  as  a 
dividend  for  the  next  division.  The  last  quotient  will  be  the 
original  number.  (See  Ex.  5,  Art.  555.) 

NOTE. — In  the  drill  exercises  in  addition,  multiplication,  and  division, 
if  the  original  number  is  a  multiple  of  9,  each  number  and  result  will  be  a 
multiple  of  9,  and  therefore  the  sum  of  the  digits  of  each  number  will  be  a 
multiple  of  9.  This  property  of  9  may  be  used  in  the  detection  of  errors. 


555, 


EXAM  PLES. 


Add 

3456 

9716 

2356 

7327 

2468 

7535 

2845 

9610 

2581 

1473 

7812 

1593 

4826 

7374 

8259 

4374 

3213 


W 

(A) 

WO 

(*) 

Add 

Add 

1000 

87  x  2 

$37.16 

347 

517 

174  x  3 

875.25 

347 

483 

522  x  4 

412.75 

694 

034 

2088  x  5 

734. 

1388* 

449 

10440  x  6 

147.03 

2429 

585 

62640  x  7 

948.26 

4511 

864 

438480  x  8 

272.72 

8328 

721* 

3507840  x  9 

371.59 

15268 

143 

2  )  31570560 

87.20 

28107 

578 

3  )  15785280 

3.16 

51703 

565 

4  )  5261760 

27.84 

95078 

013 

5  )  1315440 

375.13 

174888* 

552 

6  )  263088 

617.37 

383088 

461 

7  )  43848 

583.14 

24657 

091 

8  )  6264 

27.48 

370 

9~)783 

344.22 

721* 

87 

5.76 

8147 

V 

298 


A  P  P  E  NDIX. 


556.   Short    method    of   finding    the  balance    of   an 
account. 

Ex.  Find  the  balance  of  the  following  ledger  account: 
Dr.  C.  E.  &  W.  F.  PECK.  Or. 


1882. 
Mar. 

16 

Merchandise. 

1192 

97 

1882. 
Apr. 

22 

Cash. 

800 

M 

80 

Sundries. 

567 

40 

" 

22 

Bills  receivable. 

1000 

" 

31 

Merchandise. 

384 

30 

May 

1 

Merchandise. 

317 

28 

Apr. 

22 

Interest. 

16 

48 

" 

17 

Cash. 

424 

79 

ii 

24 

Merchandise. 

846 

51 

July 

1 

Balance. 

852 

8i 

May 

17 

'• 

387 

25 

3394 

91 

3394 

91 

July 

1 

Balance. 

852 

84~ 

ANALYSIS. — It  can  readily  be  seen  that  the  debit  side  is  greater;  therefore 
add  that  side  first  and  write  the  sum  as  the  total  or  footing  of  each  side. 
Then  pass  to  the  other  side  of  the  account.  The  sum  of  the  first  column  is 
17,  which  subtracted  from  the  next  higher  number,  21,  ending  with  1,  the 
corresponding  figure  of  the  total,  leaves  4,  which  write  as  the  first  figure  of 
the  balance,  carrying  the  2  to  the  next  column.  (If  the  right-hand  figure  of 
the  sum  of  any  column  is  the  same  as  the  corresponding  figure  of  the  total, 
subtract  it  from  itself,  and  not  from  the  next  higher  number  ending  with  the 
same  figure ;  or  write  0  in  the  balance  and  carry  the  left-hand  figure  of  the 
sum.)  The  sum  of  the  figures  in  second  column  plus  2  carried  is  11,  which 
subtracted  from  19  leaves  8,  the  second  figure  of  the  balance.  Proceed  in  like 
manner  until  all  the  figures  of  the  balance  are  obtained.  Prove  by  adding 
all  the  numbers,  including  the  balance. 


EXAMPLES. 

557.  Find  the  balances  of  the  following  accounts  : 

(1.)  (*.)  (3.) 


Dr. 


Or. 


Dr. 


Dr. 


817.20 

812.20 

237.25 

112.27 

1075. 

375.60 

222.22 

214.13 

900. 

218.36 

2318.42 

218.24 

427.30 

375. 

800. 

717.49 

812.10 

717.37 

810.75 

412. 

718.24 

648. 

938.40 

244.45 

416.30 

717. 

218.75 

118.75 

4312. 

946.33 

225. 

538.98 

222.48 

719.46 

203.13 

108.75 

SHORT    METHODS.  299 

SHORT     METHODS     IN     MULTIPLICATION. 

558.  To  multiply  any  number  of  two  figures  by  n. 

559.  RULE. — Place  the  sum  of  its  digits  between  them 
when  the  sum  is  less  than  10.     When  the  sum  is  10  or 
more  than  10,  write  its  right-hand  figure  in  the  second 
place  and  carry  one  to  the  left-hand  figure  of  the  multi- 
plicand. 

EXAMPLES. 

560.  1.  Multiply  34  by  11. 

ANALYSIS. — 3  +  4  =  7,  which  placed  between  3  and  4  produces  the 
product  374. 

2.  Multiply  68  by  11. 

ANALYSIS. — 6  +  8  =  14.  Write  4  in  the  second  place  and  carry  1  to 
the  6,  the  left-hand  figure  of  the  multiplicand  producing  the  product  748. 

3.  Multiply  the  following  numbers  by  11  :  24,  16,  18,  32,  43, 
33,  72,  81,  37,  44,  92,  87,  93,  64,  35,  36,  47,  17,  and  19. 

561.  To  multiply  any  number  by  n. 

562.  KULE. —  Write  the  1st  7*ight-hand  figure,  add  the 
1st  and  2nd,  the  2nd  and  3rd,  and  so  on ;  finally  write 
the  left-hand  figure,  carrying  as  usual. 

EXAMPLES. 

563.  1.  Multiply  783742  by  11.  Ans.  8621162. 

ANALYSIS. — Write  the  right-hand  figure  2  ;  for  the  remaining  figures  of 
the  product,  add  2  to  4,  4  to  7,  7  to  3,  3  to  8,  8  to  7,  and  write  the  left-hand 
figure,  carrying  when  necessary. 

2.  Multiply  the  following  numbers  by  11  :— 245,  346,  325,  416, 
784,  517,  875,  918,  4218,  7324,  7218,  1728,  4375,  and  8376. 

564.  To  multiply  by  any  number  of  two  figures  ending 
with  i. 

565.  EULE.- — Multiply  by  the  tens  of   the  multiplier, 
writing  the  product  under  the  multiplicand  one  place  to  the 
left,  and  add.     Or, 


300  APPENDIX. 

Write  as  the  first  figure  of  the  product  the  unit  figure  of 
the  multiplicand ;  multiply  each  figure  of  the  multipli- 
cand by  the  tens  of  the  multiplier,  and  at  the  same  time, 
add  mentally  to  each  product  the  figure  to  the  left  of  the 
one  multiplied,  carrying  as  usual. 

EXAM  PLES. 

566.  1.  Multiply  456  by  61. 

1ST  OPERATION.     2ND  OPEKATION.  ANALYSIS,  2ND  METHOD. -Write  6  in  the 

456  X  61  product.     6x6  +  5  =  41.     Write  1  and  carry 

2736  61  4.     6x5  +  4  (carried)  +4  =  38.     Write  8  and 

27816  27816  carry  3.     6  x  4  +  3  (carried)  =  27. 

Multiply  Multiply 

2.     864  by  61 ;  by  41.  5.     2345  by  121 ;  by  111. 

8.     717  by  31 ;  by  71.  6.     7416  by  51 ;  by  81. 

4.     447  by  21 ;  by  81.  7.     8324  by  41 ;  by  21. 

NOTE. — When  the  multiplier  is  any  digit,  any  number  of  ciphers,  and  1, 
the  above  principle  may  also  be  applied. 

Multiply  Multiply 

8.  375  by  301 ;  by  401.  11.     48  by  701  ;  by  801. 

9.  425  by  201 ;  by  101.  12.     376  by  201 ;  by  901. 
10.     46  by  601 ;  by  501.  18.     87  by  3001 ;  by  4001. 

567.  To  multiply  by  any  number  between  12  and  20. 

568.  RULE. — Multiply  by  the  units  of  the  multiplier, 
writing  the  product  under  the  multiplicand  one  place  to 
the  right,  and  add.     Or, 

Multiply  the  units  of  the  multiplicand  by  the  units  of 
the  multiplier,  write  the  units  of  the  product,  and  carry 
the  tens,  if  any,  to  the  next  product ;  multiply  the  remain- 
ing figures  of  the  multiplicand  by  the  units  of  the  multi- 
plier, and  at  the  same  time  add  mentally  to  each  product 
the  figure  to  the  right  of  the  one  multiplied,  carrying  as 
usual ;  finally,  to  the  left-hand  figure  of  the  multiplicand, 
add  the  number  to  be  carried,  if  any,  and  write  the  result. 


SHORT   METHODS.  301 


EXAMPLES. 

569.  1.  Multiply  456  by  18. 

1ST  OPERATION.     2NI>  OPERATION.  ANALYSIS,      2ND      METHOD.  -  8    X    6   =  48. 

Write  8  and  carry  4.'    8x5  +  4  (carried)  +  6  = 

3648  18  50.     Write  0  and  carry  5.     8  x  4  +  5  (carried) 

8208  8208  +5  =  42.     Write  2,  and  carry  4.     4  +  4  =  8. 

Multiply  Multiply 

2.  785  by  13  ;  by  17.  6.  1234  by  14  ;  by  16. 

S.  378  by  14  ;  by  16.  7.  2345  by  16  ;  by  18. 

4.  522  by  15  ;  by  19.  8.  3456  by  19 ;  by  13. 

5.  376  by  18  ;  by  16.  9.  7891  by  17 ;  by  15. 

NOTE. — The  above  principle  may  also  be  applied  when  the  multiplier 
consists  of  1,  one  or  more  ciphers,  and  a  digit. 

Multiply  Multiply 

10.  875  by  101  ;  by  108.  14.     147  by  1008  ;  by  1001. 

11.  936  by  102  ;  by  103.  15.     385  by  1004  ;  by  1007. 

12.  877  by  104  ;  by  106.  16.     783  by  1005  ;  by  1003. 
18.    '736  by  105  ;  by  109.  17.     546  by  1007  ;  by  1006. 

570.  To  multiply  by  any  number  ending  with  9. 

571.  RULE. — Multiply  by  1  more  than  the  given  multi- 
plier, and  from  the  result  subtract  the  multiplicand. 


EXAMPLES. 
572.     1.  Multiply  387  by  49. 

OPERATION. 

387  product  by    1 

19350        "       "  50  (See  Art.  43,  Ex.  13.) 
18963  49  (Subtracted  downwards.) 

Multiply  Multiply 

2.  76  by  49  ;  by  39.  5.  312  by  19  ;  by  89. 

3.  87  by  29 ;  by  99.  6.  427  by  39  ;  by  79. 

4.  45  by  59  ;  by  69.  7.  825  by  29 ;  by  69. 


362  APPENDIX. 

573.  To  multiply  by  any  multiple  of  9  less  than  90. 

574.  RULE.  — Multiply  by  the  multiple  of  ten  next  higher 
than  the  given  multiplier,  and  from  the  result  subtract  one- 
tenth  of  itself. 

EXAMPLES. 

575.  1.  Multiply  785  by  63. 


OPERATION. 

785 

70 

54950  product  by  70 
J5495  "  "  _7 
49455  63 

Multiply 

&     67  by  18 ;  by  27. 

8.     34  by  36 ;  by  45. 

4.  77  by  54;  by  63. 

5.  84  by  72;  by  81. 


576.  To  multiply  by  25. 


ANALYSIS.— 63=70-7.  785  x  70  =  54950. 
Divide  54950  by  10  by  placing  its  digits  one 
place  to  the  right.  54950-5495  =  48455. 


Multiply 

6.  345  by  36 ;  by  45. 

7.  567  by  18  ;  by  72. 

8.  518  by  27  ;  by  63. 

9.  724  by  54  ;  by  81. 


577.  RULE. — Add  two  ciphers  and  divide  the  result  by 
4-  Or, 

Divide  the  number  by  4  /  if  there  is  no  remainder  add 
two  ciphers;  if  there  is  a  remainder  of  1,  add  25 ;  of  2, 
add  50;  of  3,  add  75. 


EXAM  PLES. 
578.     1.  Multiply  446  by  25. 

OPERATION.  ANALYSIS.— Since  25  is  equal  to  100  divided  by  4,  multi- 

plying by  100  and  dividing  the  result  by  4,  is  the  same  as 
11150  multiplying  by  25. 

2.  Multiply  the  following  numbers  by  25 :— 24,  36,  37,  49,  62, 
387,  448,  512,  746,  424,  817,  937,  544,  717,  318,  324,  256,  556, 
9224,  8378,  5280,  1728,  5648. 


SHORT   METHODS.  303 

579.  To  multiply  by  125, 

580.  KULE. — Add  three  ciphers,  and  divide  by  eight. 

EXAMPLES. 

581.  1.  Multiply  637  by  125. 

OPERATION.  ANALYSIS.— Since  125  is  one-eighth  of  1000,  multiplying 

8  )  637Q(         by  1000  and  dividing  the  result  by  8,  is  the  same  as  multiply- 
79625      inS  by  125. 

2.  Multiply  the  following  numbers  by  125  :— 32,  48,  76,  87,  92, 
88,  112,  147,  317,  324,  325,  378,  419,  516,  875,  819,  725,  717,  998, 
444,  1234,  5287,  7326,  8317,  1728. 

582.  To  multiply  by  any  number  one  part  of  which  is 
a  factor  of  another  part. 

EXAM  PLES. 

583.  1.  Multiply  576  by  287. 

OPERATION. 

576 

287 


4032  product  by       7. 

16128          "       "     28  =  4  times  product  by  7. 
165312         "        "   287. 


OPERATION. 

567 


2.  Multiply  567  by  936. 

567 
936 

5103   product  by   9. 

_20412    "   "  36  —  4  times  product  by  9. 

530712    "   "  936. 

Multiply  Multiply 

3.  227  by  369 ;  by  427.  8.  932  by  183  ;  by  927. 

4.  516  by  246 ;  by  568.  9.  718  by  284  ;  by  832. 

5.  344  by  126 ;  by  124.  10.  529  by  546  ;  by  756. 

6.  728  by  426  ,  by  189.  11.  638  by  217  ;  by  618. 

7.  325  by  147  ;  by  273.  12.  435  by  248  ;  by  428. 


304  APPENDIX. 

584.  To  multiply  by  any  number  near  and  less  than 
100,  1000,  etc. 

585.  The  Complement  of  a  number  is  the  difference  between 
the  number  and  the  unit  of  the  next  higher  order. 

586.  RUEE. — Add  to  the  multiplicand  as  many  ciphers 
as  there  are  ciphers  in  the  unit  next  higher  than  the  mul- 
tiplier, and  from  the  result  subtract  the  product  obtained 
by  multiplying  the  multiplicand  by  the  complement  of  the 
multiplier. 

EXAM  PLES. 

587.  1.  Multiply  456  by  98. 

OPERATION. 

45600  product  by  100. 

912    "   "  _2. 

44688    "   "  98. 

Multiply  Multiply 

&     77  by  99  ;  by  93.  6.     387  by  93  ;  by  999. 

3.  84  by  98  ;  by  95.  6.     416  by  95  ;  by  994. 

4.  72  by  94 ;  by  96.  7.     528  by  93  ;  by  992. 

588.  To  multiply  together  two  numbers,  whose  mean 
number  may  be  squared  mentally. 

589.  EULE. — From  the  square  of  the    mean  number, 
subtract  the  square  of  the   difference  between  the  mean 
number  and  one  of  the  given  numbers. 

NOTE. — This  rule  depends  upon  the  algebraic  formula,  (a  +  b)x(a— 6)  = 
a*-b*. 

EXAM  PLES. 

590.  1.  Multiply  37  by  43.  Ans.  1591. 

ANALYSIS. — The  mean  number  is  40.  Its  square  is  1600.  The  square  of 
8,  the  difference  between  the  mean  number  and  one  of  the  numbers,  is  9. 
1600-9  =  1591. 

Multiply  mentally 

2.  87  by  73.  5.  93  by  87.  8.  112  by  108. 

8.  63  by  57.  6.  42  by  38.  9.  116  by  124. 

4.  22  by  18.  7.  48  by  52.  10.  115  by  105. 


SHORT   METHODS. 


305 


CKOSS  MULTIPLICATION-. 

591.  Cross   Multiplication  depends  upon  the   following 
principles : 


Units        multiplied 

by  units 

produce  units. 

Tens 

"   units 

L    « 

tens. 

Units 

"   tens                   J 

Hundreds          " 

"  units 

I 

Tens 

"   tens 

L        "       hundreds. 

Units 

"  hundreds 

1 

Thousands        " 

"   units 

Hundreds 
Tens                  " 

"   tens 
"   hundreds 

L       "       thousands. 

Units 

"   thousands 

Ten-thousands  " 

'  '    units                 i 

Thousands        " 

"   tens 

Hundreds 

"  hundreds 

_ 
\-       "       ten-thousands. 

Tens 

"   thousands 

Units 

"   ten-thousands  j 

Etc.,  etc. 


Ex.     Multiply  68  by  74. 


Ans.  5032. 


OPERATION. 

68 

74 


ANALYSIS. 


4x6  +  3  (carried) 


4x8  =  3 

7x8  =  8 


5032 


7x6  +  8  (carried)  =  50 


Ex.    Multiply  579  by  42. 


Ans.  24318. 


OPERATION. 

579 

42 

24318 


2x9  =  1 

2x7  +  1  (carried)  +4x9  =  5 
2x5  +  5  (carried)  +4x7  =  4 


Ex.     Multiply  567  by  348. 


4x5  +  4  (carried)  =  24 


Ans.  197316, 


OPERATION. 


567 
348 


8x5  =  40  8x6  =  48  8x7  =  56 
4x5  =  20  4x6  =  24  4x7  =  28 


197316   3x5  =  15  3x6  =  18  3x7  =  21 
19  7  3 


306  APPENDIX. 

592.  To  multiply  together  numbers  of  two  figures 
each  whose  units  are  alike. 

Ex.     Multiply  76  by  46.  Ans.  3496. 


OPERATION.  ANALYSIS. 

76  6  x  6  =  3 

46  6x7 


6x4 


6x11  +  3  (carried)  =  6 


9 


4x  7  +  6  (carried)  =  3    4 
Ex.     Multiply  135  by  65.  Ans.  8775. 

OPERATION.  •         ANALYSIS. 

•135  5x5=2 


\  *~x™  +  2  (carried)  =  9 


8775  * 

6x13  +  9  (carried)  =  87 

593.  RULE. — Multiply  units  by  units  for  the  first  figure 
of  the  product,  the  sum  of  the  tens  by  units  for  the  second 
figure,  and  tens  by  tens  for  the  third  figure,  carrying  when 
necessary. 

EXAMPLES. 

594.  Multiply 

1.  56  by  56  ;  72  by  32  ;  94  by  44. 

2.  65  by  75  ;  87  by  37  ;  46  by  36. 

3.  99  by  49  ;  85  by  75  ;  34  by  24. 

4.  47  by  37  ;  67  by  57  ;  85  by  45. 

5.  125  by  65;   126  by  36  ;   154  by  84. 

6.  76  by  76  ;  36  by  36  ;  114  by  114. 

595.  To  multiply  together  numbers  of  two  figures 
each,  whose  tens  are  alike. 

Ex.     Multiply  87  by  85.  Ans.  7395. 

OPERATION.  ANALYSIS. 

87  5x7  =  3 

_85  8x5 

7395  8x7 

8x     8+9=73 


SHORT    METHODS.  307 

Ex.     Multiply  127  by  122.  Am.  15494. 

OPERATION.  ANALYSIS. 

127  2  x    7  =    1 

122  12  x  2  >  „ 

„  >  12  x     9  +    1  =  10 
15494  12  x  7  5 

12  x  12  +  10  =  15    4 

596.  KULE. — Multiply  units  by  units  for  the  first  figure 
of  the  product,  the  sum  of  the  units  by  tens  for  the  second 
figure,  and  tens  by  tens  for  the  remaining  figures,  carrying 
when  necessary. 

EXAMPLES. 

597.  Multiply 

1.  87  by  82  ;  81  by  87  ;  65  by  63. 
&  47  by  44  ;  56  by  52 ;  58  by  57. 
8.  73  by  76 ;  79  by  75 ;  68  by  63. 
4.  44  by  43  ;  52  by  55 ;  67  by  63. 

6.     116  by  117  ;  107  by  105;  125  by  122. 

598.  To  multiply  together  two  numbers  whose  tens 
are  alike,  and  the  sum  of  whose  units  is  ten. 

599.  RULE. — Multiply  the  units  together  for  the  two 
right-hand  figures  of  the  product,  one  of  the  tens  by  1  more 
than  itself  for  the  remaining  figures. 

EXAMPLES. 

GOO.     1.  Multiply  76  by  74.  Ans.  5624. 

ANALYSIS.  —  6  x  4  =  24,    the  two  right-hand  figures  of  the  product. 
6  x  7  (6  +  1)  =  42,  the  remaining  figures. 

Multiply  mentally 

2.  24  by  26 ;  85  by  85  ;  128  by  122. 

3.  17  by  13  ;  94  by  96  ;  112  by  118. 

4.  34  by  36 ;  37  by  33 ;  104  by  106. 

5.  25  by  25 ;  43  by  47 ;  143  by  147. 

6.  35  by  35 ;  56  by  54 ;  152  by  158. 


308  APPENDIX. 

6O1.  To  multiply  by  means  of  complements  (585). 
Ex.     Multiply  991  by  996. 

OPERATION.  ALGEBRAIC  MULTIPLICATION. 

991..  9         991  =  1000  —  9 


Q  N 

"   >  sum  =  2000  — 


996. .4         996  =  1000   '  '  w L3 

987036  1000  x  1000  —  9  x  1000 

' —  4  x  1000  +  36 

(1000  —  13)  x  1000     +  33 

ANALYSIS. — From  the  above  algebraic  multiplication,  it  is  observed : 
1st,  that  as  many  of  the  right-hand  figures  as  there  are  ciphers  in  the  unit  of 
comparison  may  be  obtained  by  multiplying  the  complements  together;  2nd, 
that  the  second  part  of  the  result  is  equivalent  to  the  sum  of  the  numbers  less 
the  unit  of  comparison  multiplied  by  that  unit. 

The  sum  of  the  numbers  less  the  unit  of  comparison  may  be  obtained  by 
adding  the  numbers  and  omitting  the  1  at  the  left-hand,  or  by  subtracting 
either  complement  from  the  opposite  number.  Thus,  991  —  4  =  987. 

602.  RULE. — From  either  nujnber  subtract  the  comple- 
ment of  the  other,  and  to  the  right  of  the  remainder  write 
the  product  of  the  complements. 

NOTES. — 1.  When  there  are  less  figures  in  the  product  of  the  comple- 
ments than  ciphers  in  the  unit  of  comparison,  write  ciphers  in  the  result  to 
supply  the  deficiency. 

2.  When  there  are  more  figures  in  the  product  of  the  complements  than 
ciphers  in  the  unit  of  comparison,  add  the  excess  on  the  left-hand  to  the 
second  part  of  the  result. 

3.  After  practice,  the  complements  may  be  omitted  in  the  operation. 

EXAMPLES. 

603.  1.  Multiply  88  by  95  ;  975  by  993 ;  9999  by  9999. 
(a.)  (b.)  (c.) 

88.. 12                         775.. 225  9999... 1 

95... 5                          993 7  9999... 1 

8360            769575  99980001 
Multiply                Multiply 

2.  97  by  99  ;  by  94.        8.  993  by  992  ;  by  994. 

8.  88  by  91  ;  by  95.        9.  990  by  991  ;  by  988. 

4.  89  by  93  ;  by  96.        10.  982  by  994  ;  by  995. 

5.  75  by  97  ;  by  98.        11.  925  by  996  ;  by  994. 

6.  92  by  98  ;  by  93.        12.  875  by  992  ;  by  993. 

7.  86  by  94  ;  by  95.        13.  847  by  990  ;  by  988. 


I  sum  =  200  +  19 


SHORT   METHODS.  309 

604.  To  multiply  together  two  numbers  of  the  same 
number  of  figures  over  and  near  100,  1000,  etc. 

Ex.     Multiply  116  by  103. 

OPERATION.  ALGEBRAIC  MULTIPLICATION. 

H6  116    =    100    +    16 

103  103  =  100  +  3 

11948  100  x^OO  -h  16  x  100 

+  3  x  100  +  48 

.  (100  +  19)  x  100    .  +  48 

605.  KULE. — From  the  sum  of  the  numbers  subtract  the 
unit  of  comparison,  and  to  the  right  of  the  result  write  the 
product  of  the  excesses. 

NOTE. — See  notes  to  preceding  rule. 

'  EXAMPLES. 

606.  1.  Multiply  124  by  104  ;  128  by  106  ;  1015  by  1006. 

(«•)  (*•)  (c.) 

124  128  1015 

104  106  1006 


12896  13568             1021090 

2.  112  by  106  ;  by  111.  7.  145  by  107  ;  by  112. 

5.  102  by  103  ;  by  104.  8.  176  by  111  ;  by  108. 

4.  122  by  108  ;  by  105.  9.  1004  by  1006  ;  by  1007. 

6.  116  by  107  ;  by  112.  10.  1125  by  1008  ;  by  1012. 
6.  118  by  101 ;  by  109.  11.  1116  by  1015  ;  by  1008.' 

6O7.  To  multiply  together  two  numbers,  one  of  which 
is  more  and  the  other  less  than  100,  1000,  etc. 

Ex.     Multiply  109  by  97. 

OPERATION.  ALGEBRAIC  MULTIPLICATION. 

109         9  excess.  109  =  100 

97        3  complement.  97 

10600  100  x  100  +  9  x  100 

27     Product  of  excess  | -  3  x  100  —  27 

and  complement.  )  (100  +  6)  x  100~       —  27 


:;r,h°+ • 


310  APPENDIX. 

6O8.  RULE. — Multiply  the  sum  of  the  numbers  less  the 
unit  of  comparison  by  that  unit,  and  from  the  product 
subtract  the  product  of  the  excess  and  complement. 


EXAMPLES. 

6O9.  Multiply  Multiply 

1.  107  by  97  ;  by  95.  6.    .  1005  by  91 ;  by  93. 

2.  112  by  96  ;  by  92.  7.     1007  by  95  ;  by  97. 

3.  116  by  94  ;  by  98.  8.     1012  by  99  ;  by  92. 

4.  108  by  91  ;  by  99.  9.     1018  by  94  ;  by  96. 

5.  115  by  99  ;  by  88.  10.     1024  by  98  ;  by  89. 


SHORT  METHODS  OF  DIVISION. 

610.  Leaving  out  the  Products. — In  long  division  the 
process  may  be  shortened  by  the  following  : 

611.  RULE. — Subtract  the  several  products  from  the  next 
number  greater  ending  with  the  corresponding  figure  in 
the  dividend,  and  carry  each  time  the  left-hand  figure  of 
the  minuend  to  the  next  product. 

NOTE. — If  the  right-hand  figure  of  any  product  is  the  same  as  the  corres- 
ponding figure  of  the  dividend,  subtract  it  from  itself,  and  not  from  the  next 
higher  number  ending  with  the  same  figure  ;  or,  write  0  in  the  remainder, 
carrying  the  left-hand  figure  of  the  product. 

Ex.     Diftde  42343014  by  973. 


42343014 
3423 


973  ANALYSIS.— The  first  quotient  figure  is  4,  by  which 

we  multiply.     4  times  3  are  12,  which  subtracted  from 
4oolo 


14  (the  next  number  greater  ending  with  4)  leaves  2. 
Write  2  in  the  remainder  and  carry  1.     4  times  7  are 


ag,  1  carried  makes  29,  which  subtracted  from  33  (the 
7784  next  number  greater  ending  with  3)  leaves  4.     Write 

000  4  in  the  remainder  and  carry  3.     4  times  9  are  36,  3 

carried  makes  39,  which  subtracted  from  42  leaves  3. 

Write  3  in  the  remainder  and  carry  4.  4  subtracted  from  4  leaves  0.  Bring 
down  3,  the  next  figure  of  the  divisor.  So  proceed  until  the  division  is 
finished. 


SHORT   METHOD  S.  311 

612.  To  divide  by  25. 

613.  RULE. — Multiply  the  dividend  by  If,  and  divide  the 
product  by  100  by  cutting  off  two  figures  from  the  right. 

Ex.     Divide  11175  by  25. 

OPERATION. 

ANALYSIS. — Since  25  is  one-fourth  of  100,  multiplying  by  4 
4        and  dividing  by  100,  is  the  same  as  dividing  by  25. 

447.00 

EXAMPLES. 

614.  1.  Divide  the  following  numbers  by  25  :  1175,  1650, 
1700,    2875,    3825,   4950,    3800,    1725,    1775,   1825,  1975,  2000, 
1650. 

615.  To  divide  by  125. 

616.  RULE. — Multiply  by  8  and  divide  the  product  by 
1000  by  cutting  off  three  figures  from  the  right. 

Ex.     Divide  21875  by  125. 

OPERATION. 

ANALYSIS. — Since  125  equals  1000  divided  by  8,  multiplying 
8       by  8  and  dividing  by  1000,  is  the  same  as  dividing  by  125. 


175.000 

EXAMPLES. 

617.  1.  Divide  the  following  numbers  by  125  :  13500,  17250, 
16375,  23500,  19875,  17625,  20000,  14125,  19375,  16250. 


618.  To  divide  by 

619.  RULE.  —  Multiply  by  8  and  divide  by  100. 

620.  To  divide  by  i6|. 

621.  RULE.—  Multiply  by  6  and  divide  by  100. 

622.  To  divide  by  33f 

623.  RULE.—  Multiply  by  3  and  divide  by  100. 


312  APPENDIX. 


EXPLANATORY     NOTES. 

624.   The  marks,  numbers,  abbreviations,  etc.,  of  the  bills  in 
Art.  278  are  explained  in  the  following  notes  : 

1.  Bill  2,  7th  item—  2177  Ibs.  Sifted  Meal  at  $1.20  per  cwt.\  8th  item— 
264^  (9  Ibs.)  bushels  Oats  at  56  eta.  per  bushel. 

2.  Bill  3,  1st  item—  16319  bu.  23  Ibs.  (f  $)  wheat.     Since  the  rate  per  bushel 
is  very  small,  the  number  of  pounds  may  be  omitted  in  the  calculations.     6th 
item—  M.,  1000  bushels. 

3.  Bill  5,  3rd  item—  10  Kits  (15  Ibs.  each)  Extra  Number  1  Mackerel  at 
$1.80  per  kit. 

4.  In  Bills  6,  7,  8,  10,  11,  and  12,  the  letters  and  numbers  on  the  margin  of 
the  bills  correspond  with  the  distinguishing  marks  and  numbers  on  the  casks, 
barrels,  kegs,  boxes,  cases,  bales,  and  bags  of  merchandise. 

5.  Bill  6,  1st  item  —       ^     I&4385  "  is  mark  and  number  upon  the  cask  ; 

1544,  gross  wt.  ;  134,  tare  or  weight  of  cask.  5th  item  —  J  foil,  put  up  in  \  Ib. 
packages  and  wrapped  in  tin  foil. 

6.  Bill  7.     The  small  figures  at  the  right  of  the  words  "bag"  and  "  bbl" 
are  the  prices  of  the  same.     3rd  item  —  121  Ibs.,  gross  wt.,  21  Ibs.,  tare,  100  Ibs., 
net  wt.    4th  item  —  112  and  109,  gross  weights  ;  22  and  20,  tare  ;  221,  total  gross 
weight;  42,  total  tare.     11th  item  —  1st  column,  gross  weight;  2nd  column, 
tare.     12th  item  —  |,  |  gallon  allowance  for  leakage. 

7.  In  bills  8,  9,  10,  and  11,  the  small  figures  represent  fourths  (quarters). 

8.  Bill  8,  1st  column,  number  of  yards  in  each  bale  or  case.    2nd  column, 
price  per  yard. 

9.  Bill  9,  1st  item  —  2  pieces  Naumkeag  Bleached  Jean  containing  48  and 
47  yards  respectively  ;  total,  95  yards  at  9  cents  per  yard. 

•    10.  In  bill  10,  the  numbers  represent  the  number  of  yards  in  the  several 
pieces. 

11.  Bill  11,1st  column,  distinguishing  aumberof  each  case.    2nd  column, 
number  of  yards  in  the  several  cases. 

12.  Bill  12.     Number  on  margin  (1789),  number  of  case.    Numbers  3458, 
2032,  etc.,  manufacturer's  distinguishing  numbers  (stock  numbers). 

13.  Bill  14,  3rd  item  —  200  carriage  bolts  of  each  of  the  following  sizes  : 
%  in.  thick  x  1  in.  long,  £  in.  thick  x  2£  long,  £  in.  thick  x  5^  Jong,  |  in.  thick 

x  5|  in.  long.  The  numbers  2.40,  2.55,  3.15,  and  3.20  represent  the  prices  per 
hundred  of  the  several  sizes.  In  the  following  items,  the  1st  fraction  repre- 
sents the  thickness  of  the  bolts,  and  the  other  numbers  on  the  same  line  the 
lengths  of  the  different  sizes.  The  numbers  above  the  lengths  represent  the 
prices  per  hundred. 

14.  Bill  15.     The  letters  and  numbers  on  the  margin  refer  to  the  num- 
bers of  the  watches.    4th  item—  numbers  222  and  208  refer  to  the  style  num- 
bers (stock  numbers)  of  the  guards  (chains),  and  the  numbers  above  (37|  and  56) 
express  the  weights  in  pennyweights  ;  $1.15  per  pennyweight. 


OF  THE 

UNIVERSITY 


UNIVERSITY  OF  CALIFORNIA  LIBRARY 


THIS  BOOK  IS  DUE  ON  THE  LAST  DATE 
STAMPED  BELOW 


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2 


2440 


183983 


